Nothing worse than dealing with car transport for one-off trips.
Whatever you do, don't operate under a tight deadline. There has to be at least 2-3 days of leeway for the delivery unless you want to pull your hair out with frustration. I know people who transport cars often and even if you rent out the whole trailer, a few days of delivery window is advisable because truckers somehow always find a way to be late. And thats not even mentioning pick up date
Would be a great roadtrip, but otherwise just about any load-board is gonna be the same, and any broker is gonna be using mostly the same loadboards unless you find a local carrier (guy with a truck, trailer, and licensing)