Here's what I think about V1
Herod,
V1 means V1.
All those planes off the ends of runways are from guys stopping after V1. Lots of people in offices with computers and simulators, and test pilots in planes with delays for decision and reaction times, well, they figured it out for us. Even if it takes 5 times more pull to get into the air in manual controls, it is a plane and meant to fly. It is far better to be in the air with manual controls than in a ball of flames off the end of the runway. And yes, I've flown planes with controls like this.
There is SO MUCH misunderstanding about what V1 means and how it is calculated and what is considered, it shocks me. If the well researched procedure is to continue after V1, then continue. V1 plus or minus 20 kts is not the time for pilots to start their own personal interpretations or flight test programs.
V1 is often limited at one end or the other by Vmcg or Vr, and of course there may or may not be additional performance available for the accelerate-stop or accelerate-go conditions, but that's not the point: You don't know.
What you do know for sure, in 99.999% of cases, is that before V1, there is time to stop, and at and above V1 there is time to get airborne. So why not just do that? For the 0.001% of the time it will not work when it is not obvious (tail fell off), so be it. But during take off is not the time to try to figure that out for a 0.001% chance you might be right.
You don't have to be that smart or good to do the right thing. Just follow the procedure.