You can skip the regionals. Unless your jobs is truly awful/unsafe and you just can't bring yourself to go to work for one more day, stick with it and keep applying to Jetblue and the others. Plenty of guys here at B6 who came directly from the corporate world, and I have quite a few buddies who went straight 91 large cabin to Southwest, United and Delta. It's not uncommon at all.

Hiring is just starting up again so don't feel bad if you don't get a call ASAP, but there is zero reason with your credentials to go sit right seat in an RJ and take a huge pay and QOL hit in the HOPES that a major airline calls you. You're competitive already with what you posted for all the major airlines. Hit every job fair, meet and greet and networking event that you can find.

My .02 would be, if your job truly sucks, start looking at other part 91 gigs while also working on Jetblue and the others. If you're flying large cabin biz then you have marketable type ratings and skills that could get you another corporate job with similar or even better pay and QOL than you already are enjoying. Worst case, JB and others never call but you found yourself a better biz jet job. Best case you get a call from the majors while also getting offered a new/better 91 job.