NoD. I don't know what type of aircraft that you operate, but if it is a B737 series, have a glance at page 3.19 of the Boeing 737 FCTM.
Among other things it states: "The PNF should closely monitor essential instruments throughout the takeoff roll and immediately announce abnormalities such as Engine Failure or Engine Fire, or any adverse condition significantly affecting the safety of flight.
The decision to reject the take off is the responsibility of the captain. If the captain is the PNF, he should initiate the RTO and announce the abnormality simultaneously".
Best of luck to your BA procedure, but I notice that there is no reference in the Boeing FCTM to sharing the decision to abort.
I would say that throughout the years of designing aeroplanes large and small, Boeing has done a great deal of research on the subject of abort processes - and along with many other operators has decided that in the best interests of flight safety, crew other than the captain are not in a position to decide an abort and execute it. Incapacitation excluded, of course.
If your sensibilities and pride are offended by the Boeing policy then perhaps you could arrange for some measured abort tests incorporating your ideas, then forward them to your CAA and the aircraft manufacturer to their consideration.
Who knows - you could even be the catalyst for changing 70 years of hard won experience of the role of the captain of the ship...