Your stuff is loaded in a Uhaul then you want to find someone to drive you, 3 cats, and the Uhaul from Fla to Or? That's quite the challenge.
My first thought was hiring a college student but that might have age issues with UHaul rental.
The next issue is spending ALL that time in the truck cab with you and your 3 cats. That's not normal truck driving nor normal taxi work. That's the kind of stuff that relatives do. Or really, really good friends.
Or someone that is also moving the same direction and needs the ride as well.
Perhaps there is a military base nearby and some soldier, sailor, or airman has orders to go thataway and could be hired to drive???
Tough problem.