Ok, I had the button meanings backwards. So, given that:
1. I recreated the table layout by copy/pasting your create statement and then re-filled it from a backup table.
2. I set the 4 fields as you described in the form builder, and disabled Ajax. I also made name unique and sortable. I also removed a passback field that I noticed was there.
When I hit that darned submit button, it still lands on /wp-admin/admin-ajax.php, even with the Ajax button unchecked.
To research deeper, I looked into my server logs (I use nginx for performance reasons), and found this:
PHP Warning: Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/var/lib/php/session) in Unknown on line 0" while reading upstream, client: **IP ADDRESS**, server: **HOST NAME**, request: "POST /wp-admin/admin-ajax.php HTTP/1.1", upstream: "fastcgi://127.0.0.1:9000", host: "**HOST NAME**", referrer: "http://**HOST NAME**/wp-admin/admin.php?page=Database_Toolkit&renderinterface=dt_intfc4cf13e14ab82d"
Doing some digging, I realized it was a server-side permissions issue in that my php session directory was not writable by my web server. Once I fixed that, all of a sudden the insert started working. I bet it will fix other strangeness as well. So now I can keep playing with this!