Thanks for taking a stab at it! I think I understand the angle you're attempting to take. May I offer a relatively contrived counterexample to poke at this a little more deeply?

Suppose I have a proposition that says, roughly, "if A and B and C then contradiction". Furthermore, suppose that A and B together are already contradictory, and B and C together are also already contradictory.

Now I can construct two proofs, one in which I use A and B (but not C) to yield the desired result, and another in which I use B and C (but not A).

In what way can we say that these two proofs are essentially the same? It appears that each uses potentially rather distinct information in order to derive the expected contradiction; it isn't clear how to go from a proof that avoids A to a proof that avoids C in a smooth way.