I think you're probably going to have to do a visa run. I'm in the reverse situation at the moment, and while I'm going to apply to switch ARCs here in Taipei (if only for kicks; yes I'm definitely a bit
), all the best advice I've had to date suggests I'm going to be visiting my favorite bar in Kowloon in the not too distant future.
If you need to do a visa run, remember to take this shit with you:
1. Enrolment certificate (jiuxue zhengming).
2. Certificate of attendence and grades (chuxi jilu)
4. A handful of photos.
5. Onward flight ticket.
And maybe think about:
6. A housing contract.
7. A tax certificate (just go to the Tax office in Taipei up from Ximending with your passport).
8. A health certificate that indicates you don't have AIDS.
9. Proof of your residency in your home country.
10. An official-looking bank statement indicating you've got enought cash to hang-out in Taiwan for the period of time you intend to.
Call ahead to the TECO you intend to visit and confirm precisely what they want. It differs from place to place.