If when you say immigration letter, you mean residence certificate, then the Bangkok Bank around the corner from immigration, was easy and almost no waiting to open a savings account. Did it 2 weeks ago. And be careful, ask the account mgr if deposits are not marked as overseas deposits. Can't remember which, but either SCB or Krungsri said they are not
I am on 90 day non o visa and opened an account with Bangkok Bank in Jomtien, Second Rd and Soi 7. Needed a resident certificate, which I was able to get with a Tm30 receipt(no contract).
Not sure how accurate this is, but I would keep the deposits going to your US Bank. If deposited in Thailand, they'll send you "proof of life" letters and if you miss it, your account is frozen. A lot of trouble to fix it
that's good to know about the no proof of overseas funding. I've had a bank account for more than 2 years and proving that would be a lot of paperwork. I just added to make it 800k, so will have over 2 months "seasoning"