Another comment, this on my first try with using the KindleUnpack plugin, which was recommended in this thread and others. I used this as an alternative to converting AZW3 to Epub.

KindleUnpack worked fine within calibre and I could read output epub files just fine. But I noticed the epub files had problems in some ereaders. For example, Google Play Books would not process and accept a number of those "shifted" epubs as uploads. Also saw issues in FBreader. I noticed a strong correlation between the complexity of the book (size, number of links, deeply nested chapters and sections, etc) and the issues with the shifted files. I did flip the target epub version in the plugin (epub2/epub3/auto-detect), but that only made a difference for a couple of the affected books.

In the end, I used Calibre to convert my AZW3 to Epub and got better results. That's because in the more complex books, I would tweak some of the conversion settings and the resulting epub files seemed to work better. Don't know if others have found that, or if I just missed something.