I found what was causing the problem in this case: we are using APC Cache and the WP APC Panel plugin for Wordpress.
I fixed it with the following steps:
- go to Wordpress->Tools->WP APC Panel
- click on the User Cache Entries tab
- then click Clear user cache
As soon as I did this, all the old "extended" content from Movable Type, that I had added through the MySQL command line, started showing up in the post edit screens.