Thanks for checking my code, John. I went through the painstaking process of disabling all plugins and re-enabling them one by one, and testing at each point.
For anyone else having this problem:
I found that the plugin W3 Total Cache was the one causing problems. On further testing, I found that it was specifically the Object Cache setting that was the culprit. When I disabled that, I could update the post title as expected.
Whew!
