Actually, 1987 was the last year of belt-drives, but in the end they were made mostly for commercial use. I recently saw one in a Holiday Inn Express in Lodi, CA with a serial of C712xxxxx. It was definitely NOT a 1977 model. The last Kenmores were made in the third quarter of 1986, and WPs went on a few more months.
About the transmission - that to me looks very much like a transmission that has been the victim of water leakage through the centerpost. I have seen and dealt with a number of these, low mileage machines or not. The culprits are the spin tube seal (which almost always goes bad - late model production or otherwise) AND the bearing seals.
What happens is fairly straight forward. All Whirlpool belt-drive machines depend on an air pocket forming under the agitator. When a machine is healthy, the air pocket forms at the top of the agitator skirt, just as it begins to rise into the center. As the seals wear, they can't trap the air as efficiently, and the escaping air allows water to rise up the centerpost. This is worsened by frequent high water levels, etc. as the higher the level, the more push-down pressure on the seals.
In 1977 and older belt-drives, the taller centerposts of these machines usually prevent (note I say "usually") contamination of the centerpost, but the short-post 1978 and later models commonly flood themselves after while. In the older machines, this is how the centerposts get rusty - water creeps up too high on the post and gets metal wet which when new stayed dry.
The first thing that fails is the spin tube seal, which will grind a wear mark ring on the agitator shaft. Later on, the bearing seals (of which there are two large seals on a short post machine and a single shallow seal on the tall post models) do the same thing on the spin tube.
Once water begins seaping into the centerpost, it works its way down to the transmission. Oil/grease from the centerpost mixes with the water and slowly covers the components underneath with grossness. Once water gets into the transmission itself, it eventually rusts the internals of the transmission enough to make a chocolate milk looking oil mixture. Some transmissions won't allow water to come in if the shaft seal is in good shape. However, if your transmission is leaking oil when the machine is layed down, it will allow water in as well.
My advice is to take apart the transmission as you plan, clean and re-oil it, then replace the two springs and the shaft seal. Definitely however, replace the spin-tube and bearing seals (not a simple job unless you have the right tools) and your machine should be good to go for another serivce "lifetime". Do not re-use a spin tube or transmission shaft if rough spots are worn on them from the old seals, as this will wear the new seals prematurely. An old agitator shaft from a short post machine can be re-used in a tall post machine where the seals mate up at different points, and vice versa.
Let me know if you need any help!
Gordon
