Some follow-up to my note 42 on this thread.

Following the advice at note 43 (thank you, USFlyerUS), I called American Airlines, using the Gold number (I have Gold status).

I was immediately connected to the options recording, without a hold, and I requested refunds.

Then, I was immediately connected to a wonderful real person on the first ring, without a hold, and she quickly processed my request to cancel my trip and process a refund.

My status is now as per notes 59 & 60: I can see Pending Review, after a re-initiate action, but check status shows nothing.