that's a fairly common engine - and in the older machines, the hydro trannies tended to crap out first. Might look around for someone parting out a tractor and picking up another identical engine to drop in that machine given that you say the rest of it is in good running shape... ?

***"would not idle smoothly when warmed up (hunted & surged)"***
For what purpose does one need a smooth idling engine?
The engines are meant to be properly run at or very near maximum governed RPM when being used.
Engine lubrication and cooling is best at governed maximum RPM.
The desire for the mythical smooth idle in these outdoor power, air cooled, modern day EPA bred engines is not a good pursuit.
Surging RPM, whether at wide open throttle, or at low curb idle throttle......is the result of a limited governor capability to "fine tune" a narrow RPM range. The governor can at best do only a continuous hunt for a sweet spot it cannot maintain.
It can however, do a very good job of holding the throttle open to maintain its maximum RPM point, and that is where you need to run.
Best operation is attained by selecting the proper transmission range to get the ground speed you want, and then shove that throttle open and let 'er eat.

I agree with rcbe about looking for a replacement used engine.
Briggs Twins are very reliable if kept up with good oil and no tinkering with governor :^)

Lots of good old engines like that around, I sold a good one for $75 this summer.

Walt Conner