Yes one of those not uncommon catch 22s in Thailand. Different banks and indeed different branches at the same bank have varying practices. You could consider to go to e.g. Siam Paragon in Bangkok and try to open a bank account there. I recently checked with Bangkok Bank branch there by phone and they just require a certified copy of your passport from your applicable consulate in Thailand. So you could get that first (may require booking of consulate appointment), then get the bank account, then pick up LTR at BOI office. The LTR notification approval letter may also help as additional evidence when opening the bank account. Shop around among a couple banks. Bangkok Bank, Siam Commercial Bank and Kasikorn Bank are considered the most foreigner friendly. Check out popular downtown places like Siam Paragon and Central World, go from branch to branch. Once you have the account, deposit sufficient money in cash right then or instruct e.g. a Wise transfer to have adequate funding for the THB50k LTR visa fee. It takes 1 - 2 hours to open the account and they help you install the mobile app as part of that. I am not entirely sure whether you can immediately get access to pay from the app on the same day, sometimes the full functionality is only enabled overnight for next day use. So I guess all of this adds up and is rather tight in terms of schedule based on your current planning.
If you are planning to stay in Chiang Mai longer term then it may be better to have a bank account there, closer to where you live, to avoid cross-province transfer fees and more flexibility to visit the branch if needed. In that case maybe fly back to BKK once you have a BOI appointment. Or if you plan to fly out of Thailand do it on your way out.
I'd suggest you keep a couple days buffer in any case, especially given the current system glitches, public holidays this week (little to no progress for the rest of the week), the growing backlog of LTR recipients and other unforeseen circumstances. Hope it works out for you, good luck.