Only U-haul will know how much they charge and they will want to know what you are pulling and what you are pulling it with.
You might be able to get a good deal from a wrecker service. Talk to them in advance and explain it's not a roadside emergency and there's no rush. Also some wrecking yards have private wreckers that aren't supposed to be for hire but will do you a favor if you slip a little "favor" in their back pocket.
WARNING WARNING WARNING
If you try to air those tires, don't stand anywhere near them. Rotted tires explode violently. Use a clip on air chuck and clip it on with the air turned off. Then get away and turn on the air and see what happens. If it fills let it stabilize a few minutes before you go near it to get the chuck. Getting to the next tire isn't as important as your life.