1. You don't need to worry about the pilot shortage... it's just getting started at the regionals, and isn't even lukewarm at the majors (yet). You have plenty of time. I wouldn't delay unnecessarily, but don't kill yourself (or go into a lot of debt).

2. Regonals don't care where you got your time, or your ratings. Unless you have serious background issues or obvious personality defects you will have your choice of regionals. You do not a school with a "relationship" with a regional... in today's market, that's just a means to funnel noobs to certain regionals. Do your own research and decide where YOU want to work and live, and choose accordingly. Consider regionals with AA flow.

Some majors seem to be granting a slight preference to civilians who got their ratings at a university flight program, but sounds like you're already past that point