Why would you believe they'd sort the visa issues for you at Delta??
Easy to promise 'chance'.. I think Delta is pretty damn expensive.
What's wrong with the place you studied at?
Why didn't you think of doing full monty up to CFI/II at school with past J1 visa options, to be able to instruct?
You're not likely to secure work visa just like that.
Doing aviation foundation course at community college on F1 visa programme, all the same time doing CFI/I at affiliated flight school (thus considered 'on campus' if working there part time after finishing the rating/cert). How about that? There are some colleges that'd waive about half of the fees for already CPL/CFI holders, ie not having to do PPL, IR etc modules theory that costs. Not cheapest way, but fairly foolproof regarding visa status. They tend to be 2yr, after first year you could get OPT 1yr work visa for 'placement' as instructor, if you need it, saving dosh that you don't need to pay for second year, since you're there for hours.
Why would you say your FAA certs are useful only for USA? You can always convert. Also, some Asian countries can validate FAA ratings more easily, for instruction.
Plenty US CFIs looking for work, considering the job market and the 1500TT thing that followed some high profile crashes in recent months. So yes, it's possible that way, but not a sure deal recipe either. I can't recommend anything, just giving you a hint, where to look.