I would of course pay for the Upgrade. On Swiss Air, I was in Business Class and at the last minute on a tour I led a few years ago, the upgrade at the gate was $ 500 each way from Business to First. United did this on a flight from DC to Rome a year or so ago as well from Business to First Class as well where there were only 4 people with full flat sleeper beds and it made a world of difference for my back. It cost me $ 500 more and it was well worth it. When I looked back at Business it looked like a cattle car (on United).

The same was true on Air Egypt
and a few other airlines I've flown. If there are empty seats in First, they will often sell them on the spot. That is the reason I asked if I approached the counter or gate and asked about a 'cash/credit card' upgrade on the spot, for payment, (not for free), if they would consider it. I would not be able to pay the full $ 14,200 price for a full First Class ticket.