Edited to show the updated code.

ProjectHolder.php

<?php
class ProjectHolder extends Page {
    static $allowed_children = array(
        'Project'
    );
    static $singular_name = 'Project Holder';
    static $plural_name = 'Project Holders';
    static $has_many = array(
        'Projects' => 'Project'
    );
}
class ProjectHolder_Controller extends Page_Controller {}
?>

Project.php

<?php
class Project extends Page {
    static $singular_name = 'Project';
    static $plural_name = 'Projects';
    static $db = array(
        'Category' => 'Varchar(100)',
        'Description' => 'Text'
    );
    static $has_one = array(
        'ProjectHolder' => 'ProjectHolder',
        'Thumbnail' => 'Crop_Thumbnail'
    );
    static $has_many = array(
        'Attachments' => 'Attachment'
    );
    public function getCMSFields() {
        $categories = array(
            'Web Design' => 'Web Design',
            'Web Development' => 'Web Development',
            'Graphic Design' => 'Graphic Design',
            'Illustration' => 'Illustration',
            'Photography' => 'Photography'
        );
        $fields = parent::getCMSFields();
        $fields->removeFieldFromTab('Root.Content.Main','Content');
        $fields->addFieldToTab('Root.Content.Main', new DropdownField('Category','Category', $categories));
        $fields->addFieldToTab('Root.Content.Main', new TextareaField('Description'));
        $fields->addFieldToTab('Root.Content.Thumbnail Image', new ImageField('Thumbnail'));
        $attachmentTable = new ComplexTableField(
            $controller = $this,
            $name = 'Attachments',
            $sourceClass = 'Attachment',
            $fieldList = array(
                'Title' => 'Title',
                'Caption' => 'Caption'
            )
        );
        $fields->addFieldToTab('Root.Content.Attachments', $attachmentTable);
        return $fields;
    }
}
class Crop_Thumbnail extends Image {
    function generateProjectThumbnail($gd) {
        return $gd->resizeByWidth(200);
    }
}
class Project_Controller extends Page_Controller {}
?>

Attachment.php

<?php
class Attachment extends DataObject {
    static $db = array(
        'Title' => 'Text',
        'Caption' => 'Text',
    );
    static $has_one = array(
        'Project' => 'Project',
        'AttachmentImage' => 'Image'
    );
    public function getCMSFields(){
      return new FieldSet(
         new TextField('Title'),
         new TextareaField('Caption'),
         new ImageField('AttachmentImage')
      );
   }
}
?>

Yikes.. Your model is a mess. Explain what you're trying to do and I can point you in the right direction.

Haha, I expected as much. I have ProjectHolder(extends Page) which can hold many Projects(extends Page). Each page has one Gallery(extends DataObject), which can in turn hold many different Attachments(extends DataObject). The ProjectHolder is to serve as a general portfolio that displays the specified Thumbnail from each Project. When clicking a Thumbnail in the ProjectHolder, the Project page is then loaded which displays the full Gallery for that Project(among other info, such as the Project category and a brief description). The Gallery is comprised of many different Attachments, each of which have a title, caption, and image.

So I started from scratch and eliminated a lot of unnecessary code in the Model and has updated my first post with the revised code. Everything is working great, except I am getting two separate error messages when I attempt to upload images as as ThumbnailImage and as an Attachment.

ThumbnailImage upload error:

[User Error] Couldn't run query: SELECT `File`.*, `Gallery`.*, `File`.ID, if(`File`.ClassName,`File`.ClassName,'File') AS RecordClassName FROM `File` LEFT JOIN `Gallery` ON `Gallery`.ID = `File`.ID WHERE (`File`.`ID` = 1) ORDER BY SortOrder ASC LIMIT 1 Column 'SortOrder' in order clause is ambiguous
GET /public_html/jonathandbaker.com/images/iframe/Project/15/Thumbnail

Line 401 in D:\xampp\xampp\htdocs\public_html\jonathandbaker.com\sapphire\core\model\MySQLDatabase.php
Source

392 	}
393 	
394 	function databaseError($msg, $errorLevel = E_USER_ERROR) {
395 		// try to extract and format query
396 		if(preg_match('/Couldn\'t run query: ([^\|]*)\|\s*(.*)/', $msg, $matches)) {
397 			$formatter = new SQLFormatter();
398 			$msg = "Couldn't run query: \n" . $formatter->formatPlain($matches[1]) . "\n\n" . $matches[2];
399 		}
400 		
401 		user_error($msg, $errorLevel);
402 	}
403 }
404 
405 /**
406  * A result-set from a MySQL database.
407  * @package sapphire

Trace

    * Couldn't run query: SELECT `File`.*, `Gallery`.*, `File`.ID, if(`File`.ClassName,`File`.ClassName,'File') AS RecordClassName FROM `File` LEFT JOIN `Gallery` ON `Gallery`.ID = `File`.ID WHERE (`File`.`ID` = 1) ORDER BY SortOrder ASC LIMIT 1 Column 'SortOrder' in order clause is ambiguous
      Line 401 of MySQLDatabase.php
    * MySQLDatabase->databaseError(Couldn't run query: SELECT `File`.*, `Gallery`.*, `File`.ID, if(`File`.ClassName,`File`.ClassName,'File') AS RecordClassName FROM `File` LEFT JOIN `Gallery` ON `Gallery`.ID = `File`.ID WHERE (`File`.`ID` = 1) ORDER BY SortOrder ASC LIMIT 1 | Column 'SortOrder' in order clause is ambiguous,256)
      Line 102 of MySQLDatabase.php
    * MySQLDatabase->query(SELECT `File`.*, `Gallery`.*, `File`.ID, if(`File`.ClassName,`File`.ClassName,'File') AS RecordClassName FROM `File` LEFT JOIN `Gallery` ON `Gallery`.ID = `File`.ID WHERE (`File`.`ID` = 1) ORDER BY SortOrder ASC LIMIT 1,256)
      Line 120 of DB.php
    * DB::query(SELECT `File`.*, `Gallery`.*, `File`.ID, if(`File`.ClassName,`File`.ClassName,'File') AS RecordClassName FROM `File` LEFT JOIN `Gallery` ON `Gallery`.ID = `File`.ID WHERE (`File`.`ID` = 1) ORDER BY SortOrder ASC LIMIT 1)
      Line 426 of SQLQuery.php
    * SQLQuery->execute()
      Line 2531 of DataObject.php
    * DataObject->instance_get_one(`File`.`ID` = 1,)
      Line 2468 of DataObject.php
    * DataObject::get_one(File,`File`.`ID` = 1)
      Line 2563 of DataObject.php
    * DataObject::get_by_id(File,1)
      Line 1045 of DataObject.php
    * DataObject->getComponent(Parent)
    * call_user_func_array(Array,Array)
      Line 565 of Object.php
    * Object->__call(Parent,Array)
    * Crop_Thumbnail->Parent()
      Line 279 of Image.php
    * Image->cacheFilename(CMSThumbnail,,)
      Line 261 of Image.php
    * Image->getFormattedImage(CMSThumbnail)
      Line 211 of Image.php
    * Image->CMSThumbnail()
    * call_user_func_array(Array,Array)
      Line 408 of ViewableData.php
    * ViewableData->XML_val(CMSThumbnail,,1)
      Line 56 of .cacheD..xampp.xampp.htdocs.public_html.jonathandbaker.com.sapphire.templates.Image_iframe.ss
    * include(C:\Windows\Temp\silverstripe-cacheD--xampp-xampp-htdocs-public_html-jonathandbaker.com\.cacheD..xampp.xampp.htdocs.public_html.jonathandbaker.com.sapphire.templates.Image_iframe.ss)
      Line 357 of SSViewer.php
    * SSViewer->process(ViewableData_Customised)
      Line 163 of Controller.php
    * Controller->handleAction(HTTPRequest)
      Line 129 of RequestHandler.php
    * RequestHandler->handleRequest(HTTPRequest)
      Line 119 of Controller.php
    * Controller->handleRequest(HTTPRequest)
      Line 277 of Director.php
    * Director::handleRequest(HTTPRequest,Session)
      Line 121 of Director.php
    * Director::direct(/images/iframe/Project/15/Thumbnail)
      Line 118 of main.php

Attachment upload error:

[Warning] Unknown class passed as parameter
POST /public_html/jonathandbaker.com/images/index/Attachment/5/AttachmentImage/EditImageForm

Line 445 in D:\xampp\xampp\htdocs\public_html\jonathandbaker.com\sapphire\core\Object.php
Source

436 	 * Prepare static variables before processing a {@link get_static} or {@link set_static}
437 	 * call.
438 	 */
439 	private static function prepare_statics($class) {
440 		// _cache_statics_prepared setting must come first to prevent infinite loops when we call
441 		// get_static below
442 		self::$_cache_statics_prepared[$class] = true;
443 
444 		// load statics now for DataObject classes
445 		if(is_subclass_of($class, 'DataObject')) {
446 			$extensions = Object::uninherited_static($class, 'extensions');
447 			if($extensions) foreach($extensions as $extension) {
448 				if(preg_match('/^([^(]*)/', $extension, $matches)) {
449 					$extensionClass = $matches[1];
450 					DataObjectDecorator::load_extra_statics($class, $extensionClass);
451 				}

Trace

    * is_subclass_of(Crop_Thumbnail,DataObject)
      Line 445 of Object.php
    * Object::prepare_statics(Crop_Thumbnail)
      Line 269 of Object.php
    * Object::uninherited_static(Crop_Thumbnail,db)
      Line 2020 of DataObject.php
    * DataObject::has_own_table(Crop_Thumbnail)
      Line 89 of ClassInfo.php
    * ClassInfo::dataClassesFor(Image)
      Line 2258 of DataObject.php
    * DataObject->buildSQL(,,,,1,)
      Line 2350 of DataObject.php
    * DataObject->extendedSQL(,,,,)
      Line 566 of File.php
    * File->instance_get(,,,,DataObjectSet)
      Line 2387 of DataObject.php
    * DataObject::get(Image)
      Line 58 of SortableDataObject.php
    * SortableDataObject->onBeforeWrite(,,,,,,)
      Line 802 of Object.php
    * Object->extend(onBeforeWrite,)
      Line 665 of DataObject.php
    * DataObject->onBeforeWrite()
      Line 251 of File.php
    * File->onBeforeWrite()
      Line 783 of DataObject.php
    * DataObject->write()
      Line 133 of Upload.php
    * Upload->load(Array,)
      Line 151 of Upload.php
    * Upload->loadIntoFile(Array,Image)
      Line 226 of File.php
    * File->loadUploaded(Array)
      Line 123 of Image.php
    * Image->loadUploaded(Array)
      Line 748 of Image.php
    * Image_Uploader->save(Array,Form,HTTPRequest)
      Line 241 of Form.php
    * Form->httpSubmission(HTTPRequest)
      Line 129 of RequestHandler.php
    * RequestHandler->handleRequest(HTTPRequest)
      Line 143 of RequestHandler.php
    * RequestHandler->handleRequest(HTTPRequest)
      Line 119 of Controller.php
    * Controller->handleRequest(HTTPRequest)
      Line 277 of Director.php
    * Director::handleRequest(HTTPRequest,Session)
      Line 121 of Director.php
    * Director::direct(/images/index/Attachment/5/AttachmentImage/EditImageForm)
      Line 118 of main.php

That could be a lot of things. Looks like your File subclass got a SortOrder column on it, which it shouldn't have since File is a sortable class to begin with. If you've made a lot of changes to your model, your best bet is to scrap the database and start over because Silverstripe doesn't delete obsolete fields.

Thanks again UC... cheers!