I've frequently changed payment cards at check out. In China, I use a foreign MasterCard on my account when making the reservation and checking in so the hold is on that but most times pay in RMB using WeChat Pay when actually checking out.

I believe it really depends whether the hotel has actually charged you or just put a hold on your credit card account. In the olden times, my pre-paid rates in, say Thailand where I would go frequently were charged a few days after I made the reservation and while they checked the card when I checked in the charge and payment had already been made some weeks or months in advance so the concept of settling up with a different payment method is moot in this scenario.

However, if they've just placed a hold on your card then settling up with another card when you check out is no problem. The hold on your card will either be cancelled or expire gracefully but it won't in any case hit your credit card bill.

At this Aloft, you should establish if they have actually charged your card or just put a hold on it. If it's the former then you'd need a refund and a second charge which may be problematic for their processes with internal approvals for refunds and the like. If it's the latter then it's BAU to cancel the hold and pay with another payment type.