Well, we're back. Remind me not to change web hosts again any time soon.
Getting set up with Pair was easy. They have more user-friendly configuration tools than EZPublishing has, I have more space to shuffle around files (enough to keep a complete backup of the whole site lying around), and their servers are noticeably faster. And we're running under cgiwrap for added security, too. (Note to self: need to write a little tutorial on setting up MT under cgiwrap. The MT documentation says you can, and I've heard crusty old sailors tell drunken tales of brave folk who have done it themseves, but there seems to be bugger all in the way of step-by-step instructions for those of us who go "cgi-wha...?")
However, I'm not happy with the way I managed the DNS change. I tried to set up redirects from the old server to the new one, but my knowledge of Apache redirects and mod_rewrite is limited. Basically, if you've been trying to access sunpig.com over the last three days (the time it takes for a server IP address change to propagate across the internet), you stood a better than even chance of seeing something closer to monkey poo than a traditional web site.
What I should have done is either shut down the entire site for that time, and presented a straightforward "out of order" page; or I should have just set up a straight copy of the old site on the new server, and not bothered with the redirects at all. Managing a seamless transition between servers is hard. I realise now that making it all work smoothly would have taken a lot more effort than I actually put in, and a lot more effort than I would have had time for. And all to avoid a personal web site having three days of down time? Not worth it.