I'd say that multi-turbine time would be a better way to build time than working as a single engine CFI. You've done your homework on Gulfstream's history and reputation, although they are out of Bankruptcy, the academy is closed, and they have aircraft on order (Saab 340s).

The new owners, Victory Park Capital, own some well known brands and appear to have the cash to keep Gulfstream operating.

Victory Park Completes Acquisition of Gulfstream International Group, Inc. | News & Press Releases | Victory Park Capital

That said, they start at $19/hr, which is not quite poverty, but after taxes it'll be close.

http://aspe.hhs.gov/poverty/11poverty.shtml