If you want 3rd world banking service, try opening an account with a US bank as a foreigner, and then try to send money overseas. Not usually something that registers with your suburban branch over there.
If the OP manages to open a USD account with a bank in this country, then he has control of the money as you suggest, and can send it to himself through whatever exchange mechanism he prefers. None of the banks are going to do this without some margin or fees, so the exercise is to find the lowest costs for the transactions he wants to do. I believe the banks are capable of giving finer spreads than he has been quoted if they want the business, but they usually need to be convinced it is in their interests to do so because of the future volume they will be doing with you.