Bangkok Bank Chiang Mai (Kad Suan Kaew Branch) has a list of minimum requirements posted, I was just there to deal with account issues. You could open account with minimum the reference letter from the US Consul
American friends hear 30 day visa exempt. Don't realize arrival day is day one, 31 day months, and set themselves up for a short overstay, very common.
Yes not to be melodramatic but it is on your "permanent record". You get a stamp in your passport. Other countries you visit or request visas from might not like that too. Only in the worst case if in the days you are on overstay if you get stopped by police you are going to have major problems.
You could do a border run and get a 30 day visa exempt, or get a roundtrip ticket to somewhere close like SIN or KUL and spend a weekend there before going back to BKK and flying back. All of that will cost more than 1900 baht, or changing you original ticket. Don't overstay, always a bad idea.
Get the 5 year Elite Easy Access. You don't have to leave Thailand to get it. It works out to 273 baht per day. Theoretically if you do an in out at the end you can get 6 years out of it so 228 baht per day.