Adding another data point to this. Had a flight to Chicago ORD for April - the return leg was cancelled. Flight-only, full "cash" payment by credit card.

Cancellation notice came through last Thursday. I submitted (via website) claim for cash refund on Friday (using the Javascript workaround) - took less than 5 minutes overall. I note the funds refunded in full to my Amex on Monday (so next business working day).

A bit of speculation on my part, but everyone who has mentioned using Amex for payment has also mentioned receiving refunds very quickly. Coincidence...?