This is a very simple argument!
If you continue the takeoff with a failure before V1 then you cannot expect to reach your screen height by the end of the TODA.
With a failure, if you reject the takeoff after V1 then you cannot expect to stop within the TORA.
If you want to use techniques you have come up with yourself or which are not endorsed by the maufacturer, then be ready for some hard questions at the inquiry.