My conclusion is that this position does not have any unique proof games. The 11.5 move SPG is not unique, and none of the proof games in 12.0, 12.5, 13.0, or 13.5 is unique.
Would you post what you have as the SUPG for the position?
Well, it appears that I did not in fact have the SPG, since my solution (14.0) is longer than every single length that you have mentioned. I tried to check the position with Jacobi but after 8 hours it still shows up as 0% progress, so I suppose you are the only one who can show us the real SPG.
One of several games in 12.5