Thanks, I really appreciate the quick and in-depth response (and good news).
I still have a few months before I'm headed back over to Taiwan so I'll use that time to see if I can find somewhere that'll take me
You might want to try this - if you have the time, go through the application process with NTNU, as Ironlady suggested, to get their letter of acceptance. Take this priceless piece of paper down to your local TECO and, fingers crossed, you should be able to land a 2-month extendable, multiple entry visa with it (most US citizens get this if they apply as a student in a university LS I think). When you finally come to Taipei, go and take a look at Shi-Da, do the placement test, and if you're not 100% happy with the place, take yourself and your money down the road to TLI or some other private LS. TLI and others are good for visa extensions, but no good for visa applications (yes, there's a certain inconsistency here - the first of many you're about to meet!).
The point of this ramble is that getting a good visa up-front is important if you want to hang around here for a while, and with a girlfriend from around these parts, you might be coming and going quite a bit over the next few years... A 2-month extendable, mulitiple entry visa will cover all the possible scenarios (most are good for up to 5 years I think). AFAIK none of the private schools will get you a decent visa, and without any documentation at all (i.e. just here for siteseeing), you're unlikely to get anything better than a 2 month nonextendable (worst case) or a single entry, 6-month extendable (best case), both of which are less than ideal.