But I can finally duplicate it. In a few simpler steps. Thanks for sticking to it until you found something reproduceable!
1) make sure Sigil is closed
2) launch Sigil (empty epub)
3) click File->New->Default|Epub2|Epub33 (doesn't matter what kind of new epub)
4) place cursor before the p tag in Code View
5) split using the shortcut or Edit->Split at Cursor
The bottom line is that the problem doesn't manifest until some tabs get closed/destroyed. Seems to get worse with each tab that gets closed (or each new epub that's created without closing Sigil and relaunching).
@Kevin: I don't know that it's necessarily another issue associated with the Create New Epub2|3 feature, because I can get it to happen without using it. Closing some open tabs in general seems to trigger it. Until you close a tab, splitting seems to work as expected.
Reproduceable on Windows 10 and Linux.