I have had a KGT mobile for 3 years on the normal monthly billed basis. At the time I went to them they were the only ones who would give an phone to a foreigner on a monthly contract without a guarantor. The policy, as it was explained to me then, is that you needed to have a job and an ARC with more than six months left to run. Ironically, KGT were later taken over by FarEastTone which, at that time anyway, had the reputation of being the least foreigner-friendly.
I have also had PHS for a few years and because I get my internet from APBB (Cable Modem) I was offered a CDMA contract. The biggest problem for me with PHS and APTelecom is that they can neither recieve nor send text messages internationally nor roam in other than in a very few countries. (I have to say that I find the software on the two PHS phones I have had counterintuitive and poor. That’s the main thing that stops me using PHS more.)
Since I came to Taiwan four years ago I have never had a guarantor for anything (including phone lines, credit cards and mobile phones). But it does mean that you usually have to go with whichever company will do business with you.
I have the sense that when you apply for stuff it can also help sometimes if you first offer your TW driving licence (and maybe Health Insurance Card) as ID. Because then you are presenting the person processing with something they easily recognise and will usually accept from TW customers in place of the National Identity Card.