That A visa on arrival switch is not possible. That I needed to go out of the country and come back with the longer 60 days tourist visa given by a Thai consulate.
I checked with three schools in Bangkok, they all told me the same thing. I know rules are a bit different in Samui. Did you find some school in Bangkok that could change the visa on arrival for you? And how long ago was that? I heard the current generation of immigration officers are quite strict.
best to book directly with airlines, all the way through to final destination - so they will get you there even if first flight is late etc. Otherwise you might find yourself stranded in Bangkok with your other flight already gone. Add on top the layer of covid regulations, so it's not worth it. You'd need to pay for insurance to get through. Stay in transit area, don't pass the frontier.
No visa on arrival. Must be tourist visa got from a consulate outside of thailand. And yes better if your passport isn't full of other thailand stamps. Perhaps get a new passport in your home country before you try.