I know you can do this with the SQLQuery object, but that makes it harder to get live/dev data appropriately.

I am trying to query data out using something like:
$posts = DataObject::get('Page', "`ClassName` IN ('EventEntry', 'NewsPage')");

But, the Date field is not named Date in one of these. So, I need to get "EventStartDate AS Date" worked in there somewhere.

My current solution is to query each of these out separately and use PHP to munge them together. Is there a built-in SilverStrip way to do this?

You could have a getDate() (or just Date()) method that returns $this->EventStartDate or $this->dbObject('EventStartDate') depending on if you want the class associated with the field or just the field value.