The Sony will have a problem if the HTML is 300kb, not the whole epub. Please keep in mind that a 300kb is quite large for pure text. If you split your file for each chapter, it should not be a problem for normal books. You don't need to rename your files to be exact like the chapter names.
On a side note, if you validate the epub you have within Sigil, what are the results? Also, try to avoid Calibre for conversions, also for epub to epub. It generates a lot of redundant codeing and can make the code quite unreadable.
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