You are close. The main reason that most people with larger tired sammies don't have spares on them is a couple of reasons. The tire is too large to clear the rear bumper, it weighs enough that it causes the tailgate hinges to tear off the corner of the tub as well as the tailgate itself to tear, and the tire mount ends up cracking.
If you are enough of a cheapskate and/or don't have the money for a bumper/tire carrier combo, you/I can reinforce the hinges and tire carrier.
If you want me to do it, I can do the reinforcing for $30 for the hinges and $50 for the tire mount, exchange is needed for both.