Virginia (Shenandoah Valley) to Phoenix Route,Thoughts?

I strongly suggest you go south and take I-10 across. Even this far south yo may get weathered in. I make this trip 4 times a year (florida to Yuma AZ) and just about know I-10 by heart. However, winter
time is always a surprise. Last year, I was snowed in while staying in Lafayette LA. I-10 was snowed and frozen and closed for 3 days.

The border patrol is no problem. You will pass thru one (in NM) east bound and one(in TX) westbound. Road is basically good except some areas in LA.

Good luck.