How about checking into a Marriott for one night, putting a $2,000 Marriott giftcard on your room, then paying for it with the Visa. You'd receive:

--- About 1,000 points for the room
--- 20,000 points on the giftcard, as long as it's on your bill.
--- 6,300 points from the Visa (3 times your bill)

I've never tried it myself, but it seems like it would fit all the requirements. And then you could use the giftcard on future Marriott stays. I'm sure you could also burn some of it on your rewards stay, in the form of meals or spa services.