>             And do you also save \shipout before \begin{document} and
> restore it afterwards as indicated by the comment by Kirill Müller?

I don't.

> In any case: if there's anything that we could put into preview.dtx to
> fix the issue from our side, that would be awesome.  Patch welcome!

I admit I haven't looked into it, but I'm afraid I won't be able to
help.

Nico.