Just to clarify, the new m36 belt did or did not fit the other one with the old belt?
The brand new M36 belts (one standard rubber and the other kevlar) did fit on both mowers. The fit was identical but it was so tight on both of them that you could not move the tensioner arm effectively to engage the drive (the arm struggled to move even a few mm, even when you adjusted the cable for maximum force).
Both mowers came with old and torn up standard rubber belts on them.
I would just go to a local bearing place and get a longer belt, just take one that doesn't fit and get one a bit longer
Is there an M or Z (as I believe thats the other compatible belt class) thats effectively a 36.5? Anyway I think your advice of going and asking a vbelt specialist is a good idea and is something I'd planned to do next I'm in town.