not an IRTA but work with an NIH lab chief in a different capacity - I asked him a while back for his advice on applying to IRTA for a friend, if this is helpful:
"openings for postbac-IRTA position are far smaller than the applicant pool. It would be good for her to have all of her online materials in place [by early january]. She should write individual faculty whose research fits with her interests. This is a bit difficult as all of the institute websites are structured differently. If she is nearby, she could even invite herself to visit a few labs."
If you apply later there's always a possibility for openings, but they also may have other people on their radar by that point, so I wouldn't wait for it.
As far as evaluating PIs/labs, see if they have an existing IRTA/mentee/post-bac of some kind you can talk to. In my experience most people are happy to put you in touch.
I don't think MD vs. MD-PhD makes a huge difference, unless you see yourself going the MD-PhD route and want someone who can tell you about that experience.