Marriott Rewards came through! Using the “Contact Us” form, I described the issue, and got this email message back the same day:
Dear [Moriens],
Thank you for contacting Marriott Guest Services.
Congratulations on fulfilling the Taste of Elite challenge of 12 nights. Your stay at the Fairfield Inn [Boondocks] from June 28-30, 2011 posted to your account after the June 30, 2011 deadline but should still be considered as part of your 12 nights stayed. I have manually upgraded your account to reflect your Gold Elite Status, valid through January 31, 2013.
You should be receiving your Gold Elite card in approximately 4-6 weeks. In the mean time, please make sure to present your account when making reservations which will reflect the Gold Elite level.
Let me know if you have any further questions.
Thank you for choosing Marriott.
Sincerely,
[Name]
Internet Correspondence Specialist
Marriott Rewards Guest Services
At the same time, my account was indeed upgraded to Gold level. (The status on the “Promotion Central” page didn't change, so the adjustment was applied to the account, not the promo.)
I'm very happy about how easy this was to fix. The Internet Correspondence Specialist pro-actively answering questions about the new account level and card was great (I didn't even ask about that in my email).
Thanks again to everyone upthread for the good advice!