Six years military, two grad school moves, and overseas job assignments, the only times I managed to beat the moving van was when the moving van was a container ship and I flew. Every other time, driving at a reasonable pace with overnight stops, the van unloaded into storage before I got there. Closest I got, I was only three hours from my destination when the van got to the warehouse and unloaded.
Many of the long haul movers run two drivers. They get paid by the ton-mile, not by the hour.
Budget mentally for destination storage and a wait for delivery. Then if you get there before the moving van, you can see it as a special boon, and rejoice.