How to create a custom content type region template? I built a sub theme based on Omega's adaptive Alpha theme. I made a content type called "project". For that content type I need to edit what gets displayed on the project detail page. What is the best way to do this?

I currently have a page--type--project.tpl.php file that I can edit, but Ideally I would like to just edit the region, like with using something like region--content--project.tpl.php file or something. Is that possible? I haven't found anything online with modifying a region based on the content type.
There is a lot of ways to accomplish your goal. I'll point some of them:

Using template files

One of them is to add the new region to your current theme and just use the modules suggested by Sohail (Delta and Context) to make the blocks to be shown in the project detail page. This means that your current theme will be a new site wide region to be used as you need.

There is some other questions that cover this:

How do I create custom regions in a theme?

Render a custom region inside node template

Using GUI

Another way to do this is by using the Display Suite module. Here goes a summary of the module description: 


  Display Suite allows you to take full control over how your content is
  displayed using a drag and drop interface. Arrange your nodes, views,
  comments, user data etc. the way you want without having to work your
  way through dozens of template files.


You can also use the Panels module suite and also the Panelizer module to achieve this goal.