I have toyed with this idea a hundred times. The simple answer: No, it just won't work.
I'll explain.
The 3 speed trans on the Cub Cadets utilizes a gear reduction housing at the front of the trans. (Unlike the F-Cubs that used a different top shaft that was coupled direct to the motor, and used a final drive (gear reduction) after the trans and before the wheel.) The 3 speed trans' first through third gears where also gear reduction. Unlike, say, a 3 speed car trans that 3 gear would be a direct drive. Putting the hydro in front of this particular trans would leave you with a slower machine than you had before, with a selection of lower yet gears. Let's just assume for a minute that the 84 tooth reduction gear on the gear drive, could be replaced with the 66 tooth reduction gear from the hydro trans, you would still be geared lower. Plus, reverse would be completely unnecessary, and should be eliminated. Deere, on the 400 used a 2 speed trans after the hydro, but it was a completely different set-up. I admit, I like what you are wanting to do, and I would like to do something similar. But using the 3 speed cub trans, isn't the way to go. My conclusion of what would have to be done, is use either a different hydro, or a different trans. I like your way of thinking though!