If your EPUB uses header tags, do an EPUB->EPUB Conversion with the default settings, especially for Structure detection, the output EPUB will have an .html per chapter. Here's an example
Input - substantive text is in 1 file - Morley_0553.html
Output - substantive text is in 43 files - Morley_0553_split_000.html → Morley_0553_split_042.html
Now you can unpack as previously suggested, perhaps after using the calibre editor to remove the unwanted artefacts.
BR