Converting a mixed encoding Word doc to a single encoding (Unicode)

I have a Microsoft Word document in Czech that is partly encoded in Unicode and partly using code page Windows 1250. I am trying to get the entire thing into Unicode. Can you help me figure out how to do this?

I have the following utility installed:

Which is all well and good, but for this to work, I have to run it on the file one sentence at a time, because it happily converts text that’s already in Unicode to… well… more Unicode. Incorrectly. Like c with a hachek (010D) gets converted to regular c (0063).

This is driving me crazy–is there a way to force the entire Word document to be consistently encoded? Or a way to detect segments that are already in Unicode, and tell the conversion macro to skip those segments?