If you have been studying for 4 consecutive months at recognized university, there should be no need to leave Taiwan to get a resident visa…in fact, i don’t even think that’s possible (though i certainly could be wrong)
Your school should supply you with all the documents you need to take to the Taipei office to have your visa changed from visitor one to resident one. From there, u will go to your local police station to get your ARC.
Doublecheck with your school, man. Maybe i’m missing something in your post, but it seems u’re making a trip to Thailand for nothing UNLESS you blew it and didn’t get the paperwork done in time before your visitor visa expired. In that case, I think u’ll need to apply for new visitor visa first and then go thru the process outlined above.