I second getting the 737 type. It's a good, free, and easy way to get your ATP provided you took your ATP written before the cutoff date. It's also one of the biggest reasons I think I got a call from Southwest with such low total time.
Have you checked the instructor box?
How about the evaluator box?
And also the Safety box?
If you can push for all three of those before you get out. They will add points to your applications.