Ah. Case solved
. Unless it's utf-8, Tidy only speaks English. No matter that there are perfectly valid encodings such as the iso-8859-* line. Tidy will either output entities or do the worst thing imaginable: reduce é to e, ą to a, ź to z... etc, for any character above ascii 127.
Tidy should come with a special warning label. It can make a grown linguist cry
The problem was actually compounded by what may be a bug in TopStyle 4. Tidy does the right thing if input is utf-8, which TopStyle officially supports now. Yet for some reason when data comes back from Tidy to TopStyle, you get "raw" utf-8, also known as garbage. If you save the changes, it's search and replace next. But it's not Tidy's fault, since HTMLPad 2008 manages to get utf-8 there and back cleanly.
Now I only need to convert a batch of files from iso-8859-2 to utf-8, *and* remove the meta charset declaration from all the files first, yay!
(Moral of the story: someone who speaks Python or Perl could probably achieve in three minutes what's taken me half a day already.)