Originally Posted by
der_saeufer
It should work, but you are waaaaay overthinking this. Oyster cards are sold at vending machines for £5. The same vending machines can refund your remaining balance
and the £5 card deposit when you leave, so the card is effectively free. Every station has at least one vending machine that sells (and tops up) Oyster cards and will accept your American credit card. Even chip-and-sign cards work
Because of capping, it's important always to use the same card--so if Apple/Google Pay doesn't work because a contactless reader is in a bad mood or your battery is flat, you start the day over at zero and could end up paying more than the daily cap.
I don't think it hurts to try tapping the physical AmEx card the first time. The best case is that it works and OP doesn't have to spend a few minutes trying to deal with a ticket machine while jetlagged. Worst case, OP pays the £5 deposit for Oyster anyway.
Anyway, in my experience NFC with my phone worked the first time close to 100% of the time. The one or two failures that I ran into resolved themselves on a second tap. This was not using AmEx of course.