Your graph didnt show up...... but thanks for trying....
I said that
V1 is already LOWER than VMCG, therefore reducing takeoff MASS will have no affect. As I see it, your Balanced V1 is less than VMCG, so you have to increase the V1, you have said that you can increase the V1 by
decreasing the Takeoff Weight, I really would like to see you explain this, because even in the world of computerized performance software, I have never seen it happen

.
the whole point of a balanced field is to give you the best chance either way,
What do you mean by the best chance either way? If this was true, why dont airbus use balanced field as default? Or even Boeing? Are you saying that their methodologies are less safe than Balanced Field?
However to use reduced thrust,
For us, reduced thrust is called Flex and it has no impact on the VMCG
Mutt