I had some experience with hydro static drives when I built concrete flat-cutting machines in the early 80s (for streets, airports). They were designed to run in one direction only. They did have a reversing feature that changed the valving internally. They use a viscous fluid (silicon?) to create the friction needed to smoothly turn the driven output shaft. Once engaged, they have the drive power of a small tank. We had our geared for about 4mph (max cutting speed for the concrete) driven by a 35HP or 65hp Wisconsin V-4s @ 1600RPM. . We also built a hot rod Chevy V-6/140hp model that ran through a Muncie 4-speed for deep cutting (swinging a 60" diamond blade) that used the same hydro drive unit with no problems.
I would suggest keeping things moving in the designed direction even if it means changing the motor.
Wish I had the room to build something like that, maybe someday....
Rick