The two key pieces of advice on this thread I can see.
1) A patch is fine, likely more desirable than a plug.
2) Put the spare on the ground and put the patched tire on the spare hanger.
Peace of mind
Buy a TPMS and use it.
A TPMS is not a license to avoid checking your tires pressures and condition before every tow and at every stop. But it does give you a status of the tires while on the road.
Nothing will stop tire damage and/ or an explosive blowout if you run over a dangerous object at highway speed.
But a TPMS will catch the vast majority of tire problems before they become dangerous.