Is it possible to reliably automatically convert the text to Traditional Chinese in a high quality way?
Other answers are focused on the difficulties, but these are exaggerated. One thing is that a substantial portion of the characters are exactly the same. The second thing is the 'simplified' forms are exactly that: simplified forms of the traditional characters. That means mostly there is a 1 to 1 relationship between traditional and simplified characters.
If so, is it going to be extremely high quality or just a good starting point for a translator to tweak?
A few things will need tweaking.
Are there open source tools (ideally in PHP) to do such a conversion?
Not that I am aware of, though you might want to check out the google translate api?
Is the conversion better one way vs. the other (simplified -> traditional, or vice versa)?
A few characters lost distinction in the simplified alphabet. For instance 麵(flour) was simplified to the same character as 面(face, side). For this reason traditional->simplified would be slightly more accurate.
I'd also like to point out that traditional characters are not solely in use in Taiwan (They can be found in HK and occasionally even in the mainland)
I was able to find this and this. Need to create an account to download, though. Never used the site myself so I cannot vouch for it.