I will chime in here.
How are the front ones? Do they spin easily?
As for your thoughts if they are correct - hard to say, but generally yes - fading is a killer. Yet, they would be smoking hot after such trip. Especially in Phoenix area.
Since you say ABS has issues, did you test it? If not, take the car to a dirt road. I bet you have plenty of nice, flat, sand covered roads in AZ. Take the car to about 30 MPH, slam the brakes. See what happens. Then do 40 MPH and start pushing brake pedal harder and harder until, even when the wheels start locking keep pushing to see if ABS is fully functional.
Pulling - I am not sure if this was covered. I do not recall if yours is AT, but what gear you are in? Did you try same test of sudden braking in neutral so that powertrain is excluded? Finally, do one more thing - pump the brake twice before hitting it hard.
I am just trying to exclude things here...