Here's my tip. Forget the Amex angle per se and start focussing on the credit cards linked to hotel programmes.

European hotels are (to a US wallet) very expensive. The Priority Club Visa comes with a 30,000 point sign-up bonus - that is enough for a free night in a Crowne Plaza, worth up to $300 easily in London or Paris. Get a card for both of you, then cancel and move on to Marriott etc.