The issue with Dreamhost is now all sorted out. I thought I would have to wait most of the day, but about 30 minutes after sorting out the payment details first thing this morning in the UK, I got a bunch of emails (some automated, and some individual ones) from the Dreamhost support folks.
I’ve very pleased with the level of service so far.
I’ve also imported this ‘old’ site into the new host.
Now I’m off to hunt down some themes, and widgets before doing the ‘big switch over’.