the 1 1/8 piston is 0.187 [3/16"] too big to fit into a 15/16" [0.937] bore master cylinder.
that said, even if one were to machine the 1 1/8" piston to fit the 15/16" master, i'm "ass"uming there would not be any structural integrity left in the piston because the basic piece would have very thin sections left in spots, due to being machined for the bigger bore to begin with.
i'm just guessing about that, because i do not have an inch and an eighth piston to compare to the fifteen sixteenth piston.
just do the right thing and get the 15/16 unit from the good doctor like you mentioned. brakes are not where you want to compromise safety.