The new site is now live.
I have biten the bullet, and migrated the DNS to point to the off-site servers.
Of course, these things never go easily. The fires around Sydney today caused some power outages; I noticed four brownouts, which caused several of the systems here to reboot, and played havoc with the upstream connections, which went down for maybe 90 minutes.
All back now, and the new site is now serving, but for what looks to be a couple of javascript errors.