So......pulled the belts off and tilted the transmissions and found that they will be an exact fit from a deck standpoint.
However the 3 speed uses (as you guessed it) a 3 position speed select cable, in addition to an independent enguagment cable connected to the operator hand bail. The hydro on the other hand uses a single variable tension cable connected in series to the speed selector then daisey chained into the operator hand bail.
To swap the transmission i'd need to swap a handle assembly that I do not have,