So to start, I greased it using a malfunctioning hand grease gun and likely one side got more grease which is causing a friction difference. I found the section in the manual you posted that shows how it comes apart but I am still not confident I understand the mechanism. Here are links that may help much better than my attached images at the bottom. There are two pages at Toro. I have not had one of these apart so I do not have the pieces stored in my head yet.
Central Transmission
www.toro.com
Outbound Section
www.toro.com
Central part of transmission link above (or Toro.jpg at bottom).
#17 is the pinion gear. That is where power comes in
#16 is the spur and Bevel gear. It looks like it relays power from the pinion to gear #18.
#18 is a 30 tooth gear. It looks like this gear transfers power to #19, the output shaft thru the "Type A groove pins" (#6)
I reviewed the wheel drive which is the outer section and the pages on it in the manual you linked. I am having trouble understanding how the clutch & washers balance power from side to side. How does power transfer from the output shaft to the thrust washer(s)? Does the one with internal tabs lock into the output shaft and then the other parts rotate/slip against it thru the friction ring and clutch?
If the parts most commonly worn can be ordered in advance then it will be easier to take it apart and put it back together - rather than take it apart, order parts, wait three weeks and try to put things back together after memory fades, even with photos. It may not even need parts, just a cleaning. Open to suggestions.
That said, don't really want to take it apart without sort of understanding how it works first. I am no stranger to mechanical things although not as dexterous and adventuresome as 30 years ago. Taking it to the shop here is almost out of the question. We have a wonderfully competent shop here a mile from the house that is busy all day long with commercial accounts. Maybe a staff of six or 8 people work there. The problem is they don't want jobs like this. The cost of labor (wages, taxes, insurance, overhead) in California is about $150 - $175 an hour, and going up. When one adds up time, including book keeping and counter time, anything that takes 3 hours of work total and a couple parts is as much as a new mower. They spend most of their time selling new equipment, doing warranty work, and servicing commercial equipment. I asked them last week if they were interesting in adjusting the valves since I had other things to get done this month and they declined. They said that it was too much work for the gain I might get even though the valves might need it after 700 hours use. On top of it in 8 months small gasoline engine equipment is outlawed in the state as to being sold or resold.