I will say this only once, and still get called a spoilsport.
You are insane if you travel your bankroll through those states as a young guy with NJ plates in a sports car. Wire it and just carry a couple grand. You so fit the profile, and in the winter stand such a good chance of a problem, that the wire fee will be well worth it.
You should invest in tire chains. They're under $50, most western states allow them in mountainous areas (even have pullouts for chain attaching and removal ) and you can sell them on cl once you get there if you want. They're also great for getting yourself out of trouble if you get into snow and can't drive out. Easy to attach and remove.
I would suggest you consider 95 south to 10 (it runs west of South the whole way, so you're making progress), then all the way across 10 until you go north in AZ. In NJ, there's an enormous investment in snow removal equipment and personnel. It's not like that past about Minnesota on the northernmost route, Iowa does ok, Missouri is hopeless, southern states suck.
States west of the line I just drew are sparsely populated and slow to clear snow. They assume nobody really needs to be anywhere fast, and many don't use salt because it eats the roads, so bad driving remains for days, even weeks after a storm. They also drive trucks, jeeps, big suv's in the winter, so they manage better than you will.
If the immediate to 3 day forecast is good (and you start with clear roads) you can probably cut over around Atlanta - Birmingham, but you want to be on 10 by Louisiana at the latest, not in OK. I lived there for a winter, their storms come up fast and hard, and they don't deal.with it well.
Texas and New Mexico is a long, boring haul, but you should make good time on the route. One decent snowstorm can strand you for a couple of days west of.the mississippi; a blizzard can stop you for a week.
I'm just sayin, as someone who's lived all over the Midwest, South, and several points West, and driven about a half million miles...take the southern route. Relax. Enjoy. Your net progress will be faster and a lot less difficult.
"If the house lost every hand, they wouldn't deal the game."