Personally I'd go to the center upright on the passenger side. But being sure that door latches are out of reach, getting a rope or halter caught can happen and is always a bad situation.
If you do move the spare, beside to cut the mounting bracket off a swell. The brackets are typically not horse friendly with the tire removed. I'd leave the tire.
Honestly I'd think the left side (drivers side) would be a better option. There's less things to worry about getting caught on. And you wouldn't have a horse right there in the tack door area.
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