Another thought -- adding a transmission cooler and flush is a great idea, but it isn't cheap either. It might be less expensive to rent a U-Haul truck and trailer, and TOW your Dodge Charger. Check into it. If you have more than 1100 lbs of household goods, it is definitely going to be cheaper to rent the truck and trailer than it will be to replace your transmission, with or without a tranny cooler! Your dad is right in this case!
Michael outlined my thoughts, exactly: head down for I-10, because that I-17 downgrade is at 6% for many miles.
Welcome to San Diego, BTW. It's a nice place to live, but warning: housing is expensive here, especially compared to anywhere-Illinois.
Donna