immigration was not consulted about the DTV. It was forced on them and they want nothing to do with it. So they'll tell you to do a border bounce if you want more days or make it so difficult to extend that it's easier to just do the border bounce.
The "official" guidelines say that it can be any bank. But the immigration offices are doing anything they can to avoid giving DTV extensions, and as you know immigration offices can set their own guidelines.
The embassy website should indicate if they only allow residents to apply.
There are only 3 locations that require payment in person, Yangon Myanmar, Vientiene Laos, and Savannakhet Laos. Every other location is online payment.
I can believe it's taking them a while given how many accounts they locked. But that you can't open an account with any other bank in Thailand if you close your Bangkok Bank account is laughable and clearly a scare tactic.