Hey there triumph and everyone else!
I am pretty much in the same boat at the moment. So triumph, I was wondering what your final solution was.
I want to live in Taiwan for the next 1 - 2 years with my (taiwanese) girlfriend that I met in Australia. Like you, I am a web-developer. I currently work for a company in Europe. I addition to that I am self employed as well.
I already mailed the “council of labour affairs” in Taiwan and they told me that I do not need a work permit if I do not work for a taiwanese company and no taiwanese company is involved in my work. They just were not very specific on the visa issue:
[color=#0040FF]“As for whether you can do teleworking while you are in Taiwan on vacation, it depends on your purpose of visiting Taiwan and what kind of visa you are granted. As a visa is normally issued for a specific “purpose of stay”, what activities the visa holder can engages in within territory of Taiwan shall be in accordance with the purpose(s) of the visa.”[/color]
I mean the taiwanese government wouldn’t know if I do work on my computer (VPN) anyway, while I am sitting in the apartment. But still, it’s good to know the official rules… 
I have been in TW for a month in march and will be going back in may.
Currently my plan is to go to Taiwan on my 90 day visa exempt entry and renew (visa run) if necessary. I actually plan to go to a university to learn mandarin, maybe I will get myself a student visa. Does anyone know by chance if I can study chinese at a university while I am there on visa exempt entry? Do the universities check your visa? Do I need a student visa to be accepted?
Other than that I read on this forum that after you have stayed in Taiwan for 183 days you have to pay taxes. Can someone please give a short summary about this tax issue? Would that even apply in my case?
Thanks a lot everyone! This forum is very helpful! 
Cheers!