Calibre's viewer is really a EPUB viewer. The conversion (temporary only) happens as it opens the book.
I suspect the book has used <h# tags other places than just the true headings (I have seen scene break marks use h6 to get them bolder

. Just use the stylesheet to
STYLE things

)
If you had more experience (this take time) under your belt, I would suggest you open the AZW with the Calibre editor and look at the code at the split point. (don't feel bad. I have been poking around the code for years and there are STILL some cases that throw me

)