Phoenix, have you ever been in North Dakota in the winter?

As one who has lived and travelled across the area you would be trying to get home through, let me give one very serious piece of advice.
Plan to hole up.

The northern plains, mountains and midwest kill people every year.
Winter here is nothing to toy with. 4 (5?) years ago, in eastern Colorado we went from 60f to -30 in two days. And it stayed in the negative numbers for over a month.

Travel in that weather is laughable, I’m sorry but there’s a lot of inhospitable country you are looking at, regardless of the weather.

Now lets consider logistics.
Assuming you had a king cab pickup, diesel fueled with a full 28 gallon tank, and a hundred gallon tank in the bed of the truck, and got 20mpg, you could cruise in on fumes. Thats assuming the roads were clear and you didn’t have to detour to cross the Missouri and Mississippi rivers anywhere. What are the chances of clear roads in a crisis?

Okay enough on all that.

Gear to get out with:
.308 rifle with .32acp adapter. With a couple of boxes of each ammo you are set for any game you run across on the ground.
Wiggys sleeping bag system.
Knife and hatchet.
Heavy duty canvas tarps.
Cook pot.
Canteens (plural)
Boots and heavy socks.
Cold weather gear.

The list is endless but these are the first musts on that list.

Sorry, 2200 miles is a long way to go.
Look at the pioneers and the covered wagons. Look at the times and routes they travelled. There is a reason for the times and routes.
There are places you couldn’t pay me to cross on foot, even on horseback its sketchy. And you’re gonna be in the thick of it.