@nitpicker330
I fail to see what your graph offers in this discussion.
The question here is about increasing thrust from Flex to TOGA. So lets look at the effects:
V1's relationship with VMCG hasn't changed as VMCG was based on TOGA.
VR and V2 were based on weight which hasn't changed and VMCA which also hasn't changed.
The only thing that has changed is the acceleration rate of the aircraft. We now reach all of the speeds earlier.
In the case of engine failure before V1 we stop the same mass from the same speed (energy) but starting at an earlier point on the runway and therefore stopping earlier.
In the case of and engine failure above V1, again this would be at an earlier point than in the FLEX case (failure at the same speed) and therefore we reach screen height earlier and subsequently our gross and net climb are above those we would have had with flex.
As many have already pointed out. The gotcha is not from flex to TOGA (RATED) but from De-rated to TOGA. In this case VMC may change and therefore the V speeds need to be checked that they are still above the minimums for the new thrust.
The bigger problem I see is the mixing of balanced and un-balanced calculations by grabbing speeds from other sources.