Posting this so that others may be able to benefit, if not already. Whenever my room fee has fallen short of the Amex promo I just ask the front desk to charge my portfolio up to the AX trigger value due to some reason. This is usually upfront upon checkin but can be done at checkout. The reason could be for many reasons - eg. proposed F&B, work min spend due to budget or even min AX spend promo (use your imagination here and adapt). Upon checkout, aware that I haven’t spent the AX trigger value, I request that the balance be refunded to my credit card. Importantly, when they ask for my credit card, I ensure that somehow it isn’t available (more imagination required here) and I refund to something like a 28D MC.
I’ve done this many time across all the hotel chains for all the AX promos over many years. I’ve only ever had one or two hotels that weren‘t accomodating (pardon the pun).