My Dad has a troy-bilt rear wheel drive mower model j860.
The two problems I found with it where the blade adapter has a built in key for the notch in the drive shaft that sheared.
Also the rear wheels would not turn. Everything else was good so I ripped out the plastic tranny and had a look-see inside. All looked good. As near as I can tell the enguage fork presses onto a bearing that presses onto the gear drive. The gear wheel is aluminum with a brass gear ring around it. It would just slip on the alum center part no matter how hard I pressed the enguage mechanism. Poor poor design.
A cheap fix might be drill a small hole through the brass into the alum and insert a screw for a pin. The only problem would be continuous drive.
My advice is get a Toro , you will be happy.