The spare tire carrier was designed for 11.00-20 tires. The M34 was the first vehicle in the series and it had 11.00 tires from the start.
Since you are prepping for a long recovery. Buy a glad hand, quick connects and such that you need to hook an air hose to the passenger rear trailer air source. With a 50 foot hose, you can do all the tires with ease. Once you get home, putting a quick connect fitting on the air line under the glove box makes it easier, but for your trip the glad hand will work.
Also, the valve for the trailer air fittings are 90° off from how most every other valve you ever moved works. When the handle is in line with the tubing, the valve is shut. Perpendicular and it is on.