Try Phoenix Air, based in Cartersville, GA (about 30 minutes northwest of Atlanta). They have added 3 G1159's (2 G-III's and 1 G-IISP) to their fleet of many G-159's and Lears in the last year and would most likely enjoy getting somebody with time in type. I would expect more additions in the Gulfstream jet side as well. Phoenix Air is very specialized flying, though; Look through their website, PM me if you have questions.
I seem to recall a G-II job being posted for Birmingham in the last couple of months but can't find it right now. Call one of the FBO's there and ask.
Also, you can always call up FSI and Simuflite, the instructors (which I expect you know some) usually get good gouge.