No spare issue, just get a cheap unidirectional off-brand mud tire in the same size.
As for the 32x11.50 SSR, that was Pika's first tire and he managed it without a lift. It rubbed, chewed his fender lips a bit, but it wasn't too nasty.
I don't know much about the Xterrains, but this picture makes it look like they can take some abuse.
"During his trip up the face of the rock, One of Jim's new Xterrains wrinkled itself around a rock. It was folded over itself and looked to be about to get pinched against his steel wheel. It was called to his attention and he backed off to get it out of harms way."
Brent