I'm perfectly comfortable mounting and unmounting wheels from my car, and I'm indeed likely to drive the big tire over to Costco to get the new tire mounted and such.

The trick is that the spare lost its air slowly over two days. I don't yet know if it's pluggable or if it's a gonner. Worst case, it needs to be replaced, and that may be very expensive. I suppose I could try to find another in a wreck yard, but then the whole point of a spare is to rescue you when you're stuck with a flat on one of your real tires. It seems pretty lame to try to save money on a used spare and later have it go and fail on you when you need it.

(Don't get me started on AAA. It takes them over an hour to show up, and that's if you're lucky. I see them as valuable not for flat tires, but instead for more serious car failures.)