3000hrs total is a big ask for a FJ mate these days. I suspect most of us will be waiting for the bar to be lowered a bit...
In my experience in bizjets, employers are less interested in the total number of hours than they used to be. More important is a type-rating and (ideally) a ticket for London City, Lugano, Sion etc. Also, number of sectors flown is also of more interest than thousands of hours of cruise time.
FJ types with not enough hours for an ATPL might be better looking at investing in a light-jet rating and (say) an LCY check to stand out amongst the other type-rated pilots applying for the job. With a logbook full of shortish FJ sorties, plus those qualifications, you would be more attractive than somebody with 5000 hours spent mostly in the cruise.
Time to command is also much shorter than in airlines - you can get command in less than a year if you are good. Even better for ex FJ might be single-pilot aircraft like C510 or C525 - I have a mate who left FAF FJs and went straight to single-pilot on C525 on private ops.
It still wouldn't be easy, but could be an easier option than airlines if you are FJ and are desperate to get out.