How do I fix the problem of routes in config.yml breaking access to Page fields?

This in my config.yml to handle routes with custom parameters (https://docs.silverstripe.org/en/3.2/developer_guides/controllers/routing/).

Director:
  rules:
    'mypage': 'MyPage_Controller'

When that rule is included in the config.yml it's not possible access fields and functions defined in the MyPage class via the MyPage_Controller or template. If I remove the rule from config.yml the fields and functions are accessible, but routes with many parameters don't work.

<?php
//MyPage class
class MyPage extends Page {
    private static $singular_name = 'My Page';
    private static $plural_name = 'My Pages';

    //Not accessible if route to controller specified in config.yml
    private static $db = array(
        'MyPageVar' => 'Int',
    );
    
     //Not accessible if route to controller specified in config.yml
     public function getMySpecialVar() {
 	 return $this->MyPageVar;
     }
    
}

//MyPage_Controller class
class MyPage_Controller extends Page_Controller {

    private static $allowed_actions = array(
        'index',
        'detail',
        'category',
        'tag',
        'search',
        'detailsearch',
    );

    private static $url_handlers = array (
        'detailsearch/$Key1/$Value1/$Key2/$Value2/$Key3/$Value3/$Key4/$Value4/$Key5/$Value5' => 'detailsearch',
    );
 
    //...
    //some other code
    //...

    /**
     * UseMyPageVar() 
     * 
     * @return Boolean
     */
    public function UseMyPageVar() {
    	//Empty if route to controller specified in config.yml
        Debug::show($this->MyPageVar);
        Debug::show($this->Title);
        Debug::show($this->Content);
        //Error if route to controller specified in config.yml
        Debug::show($this->getMySpecialVar());
        
        return true;
    }

}

Fields also are not accessible in template if route specified in config.yml

<!-- ok if no route specified, empty if route specified in config.yml -->
<p>MyVar: {$MyPageVar}</p>
<p>Title: {$Title}</p>
<p>Content: {$Content}</p>

In case anyone having the same problem checks this thread, here's the code I'm using to access Page fields in the Controller

//MyPage_Controller class
class MyPage_Controller extends Page_Controller {

    private $_page; //holds reference to page that's lost with custom routing        

    //ContentController uses route, which has been changed to
    //   'MyPage_Controller' by routing rule, to initialize 
    //   page reference. Can't find anything so reference
    //   not set. (set to -1)
    public function init() {
        parent::init();

        //Initialize using default route overwritten in routing rule
        //    This will break if URL segment changed in CMS  
        $route = array_search($this->URLSegment,
                        Config::inst()->get('Director', 'rules'));
        $link = str_replace($this->URLSegment, $route, $this->Link());
        $this->_page = $this->Page($link);
    }


    //Use private var to access page fields 
    public function MyPageVar() {  
        Debug::show($this->_page->MyPageVar);
    }

    //expose $Content to templates
    public function Content() {
        return $this->_page->Content;
    }

    //Can't use Title() so expose Page Title as $PageTitle
    public function PageTitle() {
        return $this->_page->Title;
    }
}