Can anyone suggest a great (ie skilled) Tradional Chinese Doctor in Taiwan for full and thorough treatment?
Thank you.

"A full and thorough treatment" for what, one wonders?
The way you've framed your question makes me think you don't understand what Traditional Chinese Medicine is.

I really have to agree with #1. "Traditional Chinese medicine" is often little more than witchdoctoring in my opinion. While I think that acupuncture might actually have some value, I am highly skeptical of the use of herbs that are often prescribed. And you need to be aware that a traditional Chinese medicine called Ma Huang, known in the west as Ephedra, is very dangerous to a minority of people. It is a stimulant that causes the heart to beat faster among other things and has been implicated in some deaths in the west. The US government banned ephedra a few years ago.
My point was less that TCM is good or bad, effective or ineffective (though it's quite true that very little of it has been subjected to rigorous scientific scrutiny). Rather, I found it funny the OP was asking for a "full and thorough treatment" as though it were a uniform practice--a Swedish massage, say--and not an elaborate diagnostic process through which a "cure" is determined by the symptoms the patient manifests. This suggests to me that the OP might be one of those Westerners who doesn't actually have anything wrong with him, but thinks acupuncture sounds neat and wants to give it a whirl.