It sounds like the answer is not so much the time to V1 or any other speed, but what is your speed after the calculated time? If it's way below V1 you have a problem but also, by definition you have enough tarmac left in which to stop because you're stopping from a slower speed.
Isn't the right solution therefore to calculate how long it should take to get to V1 - if your speed is below V1 after x seconds then reject the takeoff?