Over or under qualified?

Maybe both.

You are over qualified for certain jobs. The employers thinks you are using them as a rest stop and doesn't want to invest time in training you (which may or may not be true - you should both be honest with each other in my opinion)

Or....you are under qualified for certain jobs because you don't yet have the ATP in hand, or your ME Turbine PIC might be a little low (you didn't break down your 4000 TT), etc....

Maybe you are targeting the wrong jobs.
As another poster responded, maybe your resume has a hidden death nail. If not a professional review, at least a trusted fellow pilot who understands the lingo should be given a shot at QC'ing your work.

From the information given in the first post, it sounds like you might be prime pickings for the Regionals (but you give you reasons for trying to avoid this route), but that leaves similar P135 jobs that you might have already looked at or serious networking for the better corporate jobs.

Good luck.