Well, I finally had the chance to try Sigil on my newest file, after going through all the other file conversions I had to get out of the way first.
I admit, I wish Sigil could handle Word-created HTML better... as I've done with manual ePub creation, I basically had to manually copy-and-paste a clean HTML file for use with the program. I had to do a few extra cleaning passes, too, as I would discover an odd character or two that Sigil didn't like (like Word's smart quotes and apostrophes).
But after that, Sigil did an admirable job of creating my file. Other than adding chapter breaks, then editing the TOCs to remove subheadings showing up as chapters, I only had to save the file as an ePub... no manual building of the rest of the ePub files, no problems with the images, nada.
One thing: The TOC links on the ePub page show up in ADE, but the links do not work... clicking on one brings you to the top of the first page. The TOC links in the ADE side menu work fine. And the file looks identical to my manually-built file in ADE, without all that manual work.
This should save me a lot of work in the future! I still have to try it out on other ePub readers, but at this point, I'm all thumbs-up!