What would a Uhaul place do, though, if you rented their truck to haul broken asphalt? Would there be potential damage issues?
And UHaul is horribly unreliable... every time I try to rent a vehicle from UHaul they don't actually HAVE it when they say it will be there.
You NEVER EVER EVER NEVER EVER NEVER EVER NEVER NEVER EVER ...... never tell them what you're doing with their stuff, and you DO take the damage waiver. The only bad part about their trucks is you'll have to move the asphalt twice. Once to load it, then you'll have to shove it off. If you rent Home Depot's trucks, the beds on 'em tilt/dump, or at least the ones in my area do.
Check out Hertz. See if they have a location in your area. We rent trucks from them all the time for work, big ones. They come specifically with a dump box and since they're just F-350's with a different back end, you shouldn't have any problems driving 'em. Bigger equipment rental shops in your area might also do trucks as well. Those are the places that'll rent skidsteers, bucket lifts, trenchers, scaffolding, etc.