I took the northern route.
Your transcontinental route looks long and dry! I have covered some of that ground on four wheels, eastbound, and I have only one piece of info for you.
In West Texas, you can decide whether to take I-10 or I-20. As far as mileage is concerned, it's a toss-up. As you will be going both ways, I suggest you take both routes. <--- That's it, the info & advice. All the rest is just bafflegab.
I took I-20, so I missed that unforgettable fortress, um, whatzitsname.
I took I-20 as far east as Jackson Mississippi, then took US49 southeast to Hattiesburg, then US98 southeast to Mobile, meeting I-10 there.
I-10 has a fine rest area, just a few miles inside Florida. This rest area has indoor toilets, and running water, some luxuries that are not always available at British Columbia's rest areas. But you will be used to that cushy stuff by then.
I can't ride those miles with you, but one of these days, I will ride them without you. I have a wicked stepson in Los Angeles, and he rates a visit from his wicked stepfather.
Best of luck!