Post revised: my Gmail is working again, thanks to the helpful work of others, so I edited the below to stick to constructive feedback.
When someone exceeds their storage quota in Gmail they should be able to pay to upgrade their storage. Not require Google Apps for Your Domain (making you have a domain, buy one through them or convert your whole company). This bundling strategy is not what I expected when I signed up for Google as an individual. I feel a degree of lock-in and forced virality that is sure to disappoint other users in the future.
One aside, when I called the Apps support line I got an educated young woman who tried to help using her knowledge of the system, not following scripts. Not sure how it will scale, but I did not expect such quality support from the get-go.