Well, as it turns out, migration wasn't so easy - the process is only partially complete. An important step remains. As described by my site host:
The resync process will involve making a full copy of the content on the original server, as-is, and placing it onto the new VPS server.
This is virtually gibberish to me . . . but I am told that this copying process is the last step and that it is to take place sometime this weekend, with no time frame yet supplied.
Please be advised that content added to the site during this time is at risk of not getting copied over. I'm not sure that this will happen (in fact, my web guru tells me this is highly unlikely), so all I can advise is to carry on as usual. If you later find an image that you posted during this time has disappeared, you can always re-post it. I don't expect any downtime, other than possibly 30 minutes or so, but - again - don't be surprised if the site is a little finicky this weekend.
As more information becomes available, I'll let you know. Thanks for your patience.
UPDATE: The copying process and migration are complete as of 11 am central, September 6, with no downtime or data loss! Woo hoo! We'll still be tinkering with optimizing resource use on the site in the next month, but I don't believe any of these actions should affect you.
