Hopefully faxing them 7 pages of docs with boarding passes, ticket receipts, and the problem history will jog their memory.
About 10 minutes after sitting down in my Coach seat, the Gate Agent came onto the plane and handed me a complimentary Gold upgrade to First Class due to the number standby passengers on he was trying to accommodate.
I thought at the time it was some serendipity to make up for what had been a very weird travel day. Didn't realize it was going to make their system choke and be such a stupid hassle to get fixed.
Update 4/20:
All the documentation I submitted apparently worked. The miles were posted as of this morning.