WOuldnt bother with the cfi/cfii if you have 1200+pic. You will get a job in the gulf quick, espically if you have some jet box time.
Lookinto Paml beach helicopters. They do a lot of forigen conversions. There are still some background and lic checks you should do ahead of time , even with your green card. Palm Beach , can crank you out quick and have a examiner on staff or easily available. Wx in fl is good and there is lots of aviation there, It is also close to the gulf.
Vortex could be an option but like HAI they are busy and it oculd take you a while to get what you want done. I am imagine you could do your CPL and IFR conversion in 1-2 weeks if you wanted to at palm Beach.
hope this helps
RB