What happens if you just ignore the silly XHTML schema, and interspersed the li with div anyway? Do browsers render it? If you make html5, us it any better?
Another choice is to detect this situation and generate div for each item, not li. That may grate with you, but in some ways the right thing to do.
Continued lists, if they are numbered, are a pain. But on the whole I guess I would lean towards stopping and starting the lists. As in fact I guess I will have to, since you note my stylesheets fail...
Carved in stone on my iPad