Those slots don't require a specific key. Put your library card in there and it'll work fine.

They get suspicious when I pay for X occupancy but request X+Y keys.

Hotels routinely give me two cards when I check in--and certainly will if I ask. I usually stick one in my wallet and one in my bag or whatever so I'm less likely to accidentally leave the card in the room.

Usually you can stick anything that has the correct form into that slot. Even thin cardboard :)