Welcome to the group, Lachlan!
It sounds like a plan for an unforgettable trip!

First of, when you say LA, I think you've meant Los Angeles (LAX) in California. Correct me if I am wrong.
Feb is cold! I have ridden on snow sometimes (several hundered miles, but not that far as you plan.
For sure, taking I-40 to cross the country will be the best route at that time of year. Temperature on the south is milder, but you will need seriously warm clothes for this trip.
Anyway, I would have this trip if I have change.

Crossing USA is always in my dreams every day, even though, I have crossed the country many times.

Good luck and let us know if you have any questions.
Nomad