Okay, thanks for the help. I'll clarify my situation a little: I originally came to Taiwan over a year ago after applying to a part time work/study fellowship in America. Unfortunately, the university that I applied to the fellowship through screwed up and sent me over here on a student visa, not a work one, and the government found out about it and naturally told me that receiving income on a student visa is illegal. After a long period of deliberation, they also told me that when my current ARC runs out I'll have to leave the country and wont be able to come back in for about 3 years. This is very distressing, especially because when I applied for my fellowship I put my trust in the university and they obviously made a big mistake. (For clarification, the school also got fined too, but the individual people involved who were teaching here still have to be punished, which is why the government is making me leave.)
I'm searching for possible ways to stay in Taiwan/re-enter in a relatively short period of time. I want to do this mainly because I was studying Chinese pretty intensely here, and also because I have a grandmother here. When discussing this over with some immigration people, they actually suggested that I just go back to America and apply for this Overseas Chinese Passport. This was the first time I'd heard of this option. When I asked them for further details, they said if I got this type of passport, I wouldn't have to do military service.
1. Ther eis an Overseas Chinese ID given by the government in the Republic of China (Taiwan). With this you get special privileges -education, jobs, etc.- and no conscription. This is usually requested at the Overseas Chinese office closest to you abroad. They make a study and determine if you are eligible. This is not a passport, just an ID.
2. Then there is the proper request of a "Taiwanese ID and passport", which refers to ordinary citizens of the Republic of China (Taiwan). This is something else. This has to be requested in Taiwan, and yes, it probably entitles you to a stint in the army.
I'm very confused about the particulars of this Overseas Chinese thing. I always assumed that if I applied for a Taiwanese passport, I would become a citizen and be obligated to serve. So actually it's just an Overseas Chinese ID, not an actual passport? And even if I got this ID, wouldn't it have to have some proof on it that I'm an American citizen, like my American passport number? My American passport number is the one that's blacklisted in Taiwan currently as a result of my work fiasco, so if that information is presented, it wouldn't do much good for me trying to re-enter Taiwan.
Ultimately I'm thinking I'm just probably going to have to head back home to America and figure things out there. The immigration people I talked to said I should be able to do this with no problem if I wanted to come back to Taiwan, but it seems like it's a lot more complicated than what they made it out to be.