From a post by LB, I learned about tree-tagger, which I've downloaded, installed, and briefly tested. It seems to work very well, producing POS-tagged text from input. I also grabbed LB's aftertag.pl PERL script, which is supposed to turn the tree-tagger output into good TEI.

Unfortunately, the PERL script doesn't want to run -- there are several errors:

syntax error at aftertag.pl line 7, near "<"
syntax error at aftertag.pl line 7, near ";) "
Unmatched ) in regex; marked by &lt;-- HERE in m/&lt;!--) &lt;-- HERE  { # tag found<br / at aftertag.pl line 10.

Figured that perhaps the HTML entities were the product of the publishing engine on LB's blog site, so replaced them with angle brackets in line 7. That left me with the line 10 error, which I still haven't figured out. I'll come back to this, because it will be really useful.