I have a Rally 5hp 22" mulching mower (model: CD4H472B) that is self propelled. At the moment, the entire gearbox is dissassembled. Why?

To start, last season I changed the drive belt. Before I did, the thing, with bald front tires, could walk itself up a hill no problem. After I changed the belt however, it wont move on its own one bit.

I took the cover off and took a look. With the wheels off the ground, they spin fine. When put down, the pulley stops spinning, along with the belt untill you start pushing it. So...

I then tore apart the gearbox. The "lube" was darn near dried to the case, and you could visibly make out the gear contact pattern. What I have seen:

The pinion off the pulley shaft (input) has alot of up and down play. Can this be shimmed to reduce it?

I have since cleaned the lower half of the case. It seems to be just grease that you would use on a zerk fitting. Is that what should be used again? Should I put vehicle gear lube in there?