First go back to the BOI LTR Visa website and read the requirements again.
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Brandon is correct, you might qualify for the Work-From-Thailand Professionals visa, but it has nothing to do with your savings. Call them if you're not clear on the requirements before you go any further. They are very helpful.
Just don't wait until the day before it expires. I've see 2 people be rejected at Immigration in Jomtien for coming in the day before expiration. Other IO's may not have this issue, but why chance it.
In addition to the info Stuart provided, here's two things to consider: 1) Most banks will charge an ATM fee if you withdraw money from an ATM outside the province of your "home bank". This can be worked around by using the ATM withdraw function on your bank's phone app, 2) Be sure that Immigration will accept your annual extension bank statement from a bank outside the province. Shouldn't be an issue but each Immigration office do their own thing, so you never know.
Whatever! You must be really bored if you felt the need to nitpick my comment. But if you can actually provide the Thai law that says that using an agent to open an account is illegal then I'll send you a beer via Thai Post.
You can't just roll up and hand them your phone, so you'll have to print it out. Might as well use the photo shops near your Immigration office, or one of the thousand Kodak shops you'll see around any town.