The two most important things in an RTO are:
Brakes and
Spoilers
Reverse is secondary.
Boneman - I think you will find that Boeing actually task the F/O with ensuring the speedbrake has deployed and the Captain with doing so(/anyway) if it has not? Your airline may of course differ.
In fact. C Titus, as you will be aware it happens PDQ, BUT there is a sequence where from closing the throttles, F/O checking bits done (including spoilers) and the hand going to 'backup' the action of the autospeedbrake - the hand then goes back to the throttles and on with the reverse.