Route #1 - Personally, I would completely scratch the idea of driving the 10 across Texas. Texas is miserable, especially in the Summer. The 10 also takes you right next to Juarez.
You don't want to be anywhere near there. Seriously. That's not a joke.
Route #2 - Takes you through Dallas. Very hot and humid during the Summer. Worse than anything Florida has to offer. (Can you tell I'm not a big fan of Texas?) Southern Alabama, Mississippi, and Louisiana are all cool places to visit, IMO, but it truly depends on your preference.
Route #3 - Takes you through Memphis. If you hit it during the day, it's awesome. If you roll through at night, keep going.
As far as I-40 is concerned, which pertains to both #2 and #3, it's pretty boring. Greg and I drove from Upper East Tennessee to Surprise in 2.5 days taking the 40 for almost 1500 miles of the trip. It's a great way to get from point A to point B but not much excitement. It's the road that killed Route 66 for convenience.
Whatever you decide, DRIVE THE PCH. It's gorgeous and a must. Do not miss it.
Whenever you get to AZ, shoot me a message. I'll check the schedule and see if we can meet up somewhere without throwing off your timeline. Our desert can be pretty awesome if you know where to go and what to see.

Hope this helps.