What brand & size of tires. Made in the USA or Chinese shit?
If you are running 20 inch Hwy Tires, I'd take 2 spares. If Chinese OR tires, I'd bring 2 spares. If 17 inch Quality US made AT or MT tires, 1 spare should be enough with a compressor (that connects to your battery terminals) and a tire plug kit. I have plugged sidewalls with my kit.
I use this one and have plugged 4 tires with it.
https://www.amazon.com/dp/B06X15JJ4FAir down your tires when going off pavement.
15 to 18psi will give your tires lots of puncture protection.

Cooper Puncture Test
Lots of states that have off road trails also have Volunteer 4x4 Rescue Groups. I'm a member of the Off Road Portal and have an app on my phone where I can request help.
https://offroadportal.org/I also receive alert to others needing help in my area. Plus I'm an Admin for the Missouri 4x4 Rescue group on Facebook that is sponsored by RhinoUSA. You might look on Facebook for the states your are going and join their 4x4 Rescue group page.
I've helped rescue 3 vehicles as part of the Missouri 4x4 Rescue group.
A Gladiator in the mud:
Attached FileA 40ft RV also stuck in the mud:
Attached FileAnd 2500 Chevy pickup stuck in a swamp down hill.
Attached File