Storing a spare where there is no place to store

There’s no need to invent a solution. YOur best bet is to just accept that your SUV doesn’t have room for a spare tire and use it as is, just the air pump kit. If you insist on carrying a spare tire (despite what the manufacture intends), and you can find a safe place to hold the tire to, suggest at a minimum to use ratchetted nylon tie-down straps rather than ropes.