Part of the problem was moving to a new host with a different directory path that is recorded in abspath.php.
I did a global search and replace of the old directory path with the new directory path in the exported SQL and then reimported the SQL.
No success.
I have two other websites with this problem and it looks like the cforms_settings just won't transfer over.
I had a backup of a form so I was able to reconstitute that one form, but I didn't have backups for all of the forms, so it looks like I will have to recreate them.