Obidiah, I don't deal with the V speeds that much, but from a more theoretical viewpoint keep in mind that when you aren't producing lift you also are not producing induced drag. Keeping the nose wheel on the runway should minimize the lift from the wings and allow you to use more thrust to accelerate. I also believe this is one of the main reasons why Vr is greater than Vmu.
As far as comparing Vs and Vmu, there are a few conditions that force them to be different. There may be a pitch limit due to the tail striking for Vmu that you wouldn't have for Vs. Ground effect plays a part with Vmu but not with Vs. Also, I believe that Vs is determined with power off and Vmu is at takeoff power (I could be wrong on these ones). Propwash flowing over the wings and vertical component of thrust would lead to differences in Vs and Vmu.
Matthew.