Fixed! Missing library.php file
I thought I had looked at all error logs on the server, but I missed one.
The PHP error log showed "Failed opening required 'library.php' "
Sure enough, the script had not installed that file in my webassist/database_management folder
It was in the ..configuration/shared/webassist... (path shortened) location, but it wasn't in my site. I have no idea how the form worked the first time, but after I copied the file into my site, the form submitted, no 500 error page, and it wrote to the database.
I love spending hours and hours and hours troubleshooting (holiday weekend, no less), only to find out that a file that should have been there wasn't...