I'm an FI (350TT)and safety pilot on Kingair's
If you are safety pilot on King Airs, it sounds to me as though you already have your 'in', no?
Contrary to how it might feel, 350 hours in the whole scheme of things is really NOT that many and unless you are exceptionally gifted, if you go on a type rating course for most biz jets - you'll probably struggle.
In your position I would sweat your nuts off to get some more hours somehow (para dropping, glider towing, take your friends on some adventures and cost share) meanwhile cultivating your King Air connection.
Impress the King Air guys with your attitude, reliability and enthusiasm and see where that goes? Could you afford to get a King Air type rating? Would the King Air guys let you fly as PIC on empty legs if you got rated?