there must be a decrease in the take-off mass to acheive this climb performance
..will depend on the circumstances but often (usually) is the case
This I would suppose give a surplus TORA and TODA.
need some care with terminology .. TORA/TODA relate to what the runway has to offer and are aircraft-independent. If you reduce weight to make a gradient requirement (at min speed schedule), then all the required runway numbers will reduce .. ie TORR, ASDR, TODR
Since V2 is the take-off safety speed which I assume varies with weight, and in this case will decrease because of the decreased weight.
down to the point where speeds become Vmc limited
Is there a procedure then to increase V2 to the speed near the best climb angle speed without offloading anything?
not necessarily a case of pegging best climb angle but we can improve climb performance .. Boeing calls it "V2 overspeed" and Airbus "improved performance". Min V2 schedules are well below best rate .. it is not feasible to go to max rate as the benefits get eaten up by runway requirements but, in general, it is useful to increase up towards, say, V2 + 20 or 30 knots if the runway length permits.
I don't know if it sounds confusing
.. don't worry .. we're all a tad confused at times ..