Mae Sai border immigration won't let you out if they won't let you in again because the Myanmar side don't give you a visa, they give you a day pass so you would be stranded in Tachileik. Also, you're not doing any kind of '90 day check' as in 90 day reporting (which reports the fact that you've been in the country for 90 days or longer) because you haven't been in the country for longer than 90 days, and can't on a visa that requires you to leave the country every 90 days. You're leaving Thailand and entering again which will get you stamped in for another 90 days, Mae Sai also don't ask for money, onward travel, or accommodation bookings.
Myanmar immigration want ฿500. They keep your passport and give you the day pass. Tell them "No shopping" and they will be quicker than usual in stamping you in, and out, and sending your passport over to the office on the other side of the road where you pick it up on your way back to Thailand. When you reach the Thai border again pick up anew TM6 at the little kiosk in the middle (fill it out on the little bench which has pens on it) before you get in the queue for the entry stamp.
the difference? The difference is that your passport number changes when you get a new passport. So the number associated with your bank account becomes obsolete and you need to update it with the bank.
Thai bank accounts have the account holders ID number associated with their account. Many foreign nationals obviously don’t have Thai ID numbers, therefore the banks use our passport numbers. These numbers change when we get a new passport. This new number then needs to be updated with our Thai banks.
Because getting an extension might be easier than going to the border? You say you can't walk so maybe going to the immigration office, with some help obviously, might be something you could do?