, lol i am not 100 % sure but i think teaching on line with no full support of a reliable school is not entitled to get a work permit, its even illegal.
i have doubt of what you try to do as it seems its to have "a more solid situation..."!
yes they can see but that is the passport holder that must check if the stamps are correct before they left. most time they do not recognise their mistake (lost face problem in the land of smile). Anyway its not a good idea to use loud voice with them, their are the boss in their country.
And if the passport is at the end the visa is not longer valid, so PP must be renew at the embassy and presented at the immigration with a letter from the embassy so Imm. will update the visa.
you have to go to konson office, make the checking, eyes, drive 100 meters backward, see few movies (in TH), all that in the morning. then afternoon if succeed you pay & get the license (first time 1 year and next 5 years)
BUT: as tourist many offices will not accept so you will need international DL for bike or car or both.
on roads the checking is rare so can take your luck BUT in case of accident you will have big problems...