Two suggestions for you, Paddlin.
When you're creating the EPUB file using Sigil, do you use the TOC editor to create the NCX table of contents? Once you've got the XHTML, CSS and image files all set up, click on "Tools" in the menu bar, then select "TOC Editor". You should see a dialog appear, listing all the elements you've coded as headings (h1, h2, etc). Deselect all of the illustrations, so that only the chapter headings are selected, then click on OK. That should either ensure that the NCX file only contains navpoints for the chapter headings, or highlight if there's a problem with the HTML coding.
Then, when you load the EPUB into Calibre, and initiate the "Convert Book" dialog, having selected MOBI output, click on "Structure Detection" in the menu on the left. At the top right of the dialog, you should see a text box labelled "Detect chapters at...". Click on the wizard button to the right of that text box, and in the top drop down in the new dialog that appears (labelled "Match HTML tags with tag name"), select "H1". Click on OK. Make any other setting changes that you want to make, then click on OK to initiate the conversion.
Those two things
should ensure that the "chapter skips" are set up for the correct points in the book. I hope!