I'm a hotel noob, but if you can reach status on 10 STAYS and a stay is equal to 1 night standalone, wouldn't it make sense to just check-in and check-out repeatedly during a multi-night stay? Sure it's annoying, but a 5 night stay is either 5 nights, or you could make it 5 stays, getting you half way there.
My best guess (I could be way off) would be that if you told the desk agent what you were doing, they might not even make you vacate the room, they'd process it and just "give" you the same room.
Also sorry, to stay OT the SPG site says gold "•An upgrade to an enhanced room at check-in — corner room, higher floor, or better view."
But I guess that doesn't necessarily mean one of the rooms that includes this club access?