It seems you've thought about this a lot, but what would be the point of extending the time spent on the take-off run to get the extra 10kts? In order to gain the 10kts extra that you've suggested you'd swallow up loads of extra tarmac. If you'd taken off at the original Vr speed you'd soon reach the Vr+10 speed. (More drag force on an aircraft with it's wheels on the ground then when it is climbing out.)
If you did an experiment where the Vr+10 take-off was compared to a standard Vr take-off you'd find that the standard aircraft would be higher and faster at a given distance than the Vr+10 aircraft. All due to an aircraft being a more efficient machine in the air than on the ground.
Hippo.