Additional information: another couple who took the same cruise with us - they also received a refund check from Princess today. But here's the important piece of information: they never requested a refund; in fact, they haven't contacted Princess at all since the cruise ended on July 8th.
Clearly, all my requests for a folio statement and refund check made NO DIFFERENCE. Princess is just processing the refunds on their own schedule, customer requests be damned. And then sending it out via snail mail (vs a credit to the customer's credit card) is just an additional insult to customers.
My wife and I have decided we will be looking at other cruise lines if/when we decide to go on another cruise. This experience is just too bad to ignore and we don't really see any value in being Platinum-level members.