Try Corporate!
I have met someone who flew 6000 hrs on Beavers or others float-types before getting a Lear 35A and a lastly a Falcon 50EX job.
Another one who flew 8000 hrs on BE99 before getting a F-27, F-28 and then fly corporate on the Falcon 10, 50 and later 50EX.
Both were very happy with their corporate job (no charter).
One in Seattle, the other in France.
Delta new hires' average flight experience, back in 1996 I believe, was around 4000TT, 1000 Jet time. So if you're not crazy about regionals (and I understand this) , the corporate world will bring to you the turbine experience you need.