Well, the crossing seems to have been successful. All my sites are now located at a new webhost, which seems to be significantly faster at loading pages etc. All the databases seem to be working, which was an area of concern. Clearly this stuff is designed to work with migrations.
Email appears to be working correctly as well.
I think the thing I’m most surprised by, is how fast the domain re-delegation has been – 2 hours. I recall it used to be a lot slower.
Anyway, we’ll see how it goes, if any issues crop up etc.