My only real problem is my ccw permit is not recognized by MN so to be legal I have to disarm and unload when traveling through that state. IL just requires a long travel reroute.
I just traveled across 11 states and the only place my permit wasn't recognized was my final destination -
MN.
(I won't go to IL for anything. I might make a mistake and spend a nickel there which could be used to support the MF'ers that run the place.)
As to the OP question, I'd take the AR. Shotguns have little advantage over handguns as far as range is concerned.
The carbine gives you hundreds of yards of influence. If you want to be more low key in the eyes of LEOs, take a lever action.
BTW, AR10s make great deer rifles! That 8 point buck never stood a chance against the 168gr Berger VLD.

So, anyone carry food supply with them? Is that paranoid too?
Lots of food, water, ammo. It's not paranoid, it's being prepared.