Only you can answer that..
Me? I would make PIC on that Hawker ASAP. One should make a min of 75K as a Hawker Captain AND you are now a jet PIC.
Whats makes you think the majors are the place to be anymore? been under a rock for the last 3 years? (kidding)...go to a regional and you can look forward to a laughable sub 20K paycheck (nice!) and be at the whim of the struggling chap 11 dip$hit operation you are feeding? nevermind the fact that you are then loggin SIC jet time - great for experience but useless when targeting major jobs.
Now, if that Hawker gig has no future (like a GV/Global) , the pay is sub NBAA, the schedule is brutal..etc...look to move on to a decent corp gig. They are hiring these days - Vietnam era guys are starting to retire...the new-hire future is very good in corporate aviation.
So basically - I would toss out that sick idea of torture at the regional airlines, become a Hawker Captain, and network around for a six-figure corporate job while waiting for your dream job (United, American, Delta..??)
just an opinion.