Chris - (this is going to be a long post)
That picture is potentially confusing a little because there are a couple seals that approximate that image that are used in various places in the spin tube and centerpost area, but it does look like the right part or at least similar to what you need. I believe the part number is 91939 from Whirlpool so check accordinly.
Your machine is 24 - 27 years old. It used to be back when they were 10-15 years old that changing the spin tube seal would solve the problem. These seemed to wear-out first. I had to do that in fact in my 1986 Kenmore 70 (which I bought new) in 1993. BUT, there is a second set of seals that are equally if not more important, which are the bearing seals in the centerpost. There are two in any 1978 and later built belt-drive washer, in fact the same seals are used in all DD machines. These take longer to wear out.
These seals are not easy to remove. I do not know of a way for certain to get them out without pulling the upper centerpost bearing as the seals come out with it. I do plan to experiment with this soon, but have not had the time. The bearing seal in older machines can be pryed out, but yours are much more substantial and are inserted into the centerpost much further. If they can't be removed without distorting the centerpost, then you'll have to do at least half a bearing job.
There are more complications unfortunately. The agitator shaft on the transmission very likely has a groove worn on it from the spin tube seal. If you seat a new seal in the tube in the same spot, the groove on the trans shaft (which is usually textured and rusty) will chew up the new seal quickly. You have to seat the seal lower, or carefully a little bit higher, OR swap a transmission in from a tall post machine and use your old transmission in the old machine - they'll both have new seal sealing surfaces that way and I've done this many times.
Finally, I may get some flack for this, but I would recommend you abandon the Roto-Swirl agitator in that machine. It wasn't made for it. Though it fits, that agitator was designed long before the short centerpost models, and it has massive air pockets under it that weak seals can't control. The DA has a very narrow center shaft, with no air pockets, and a weap hole in the base to allow what air does accumulate under the agitator skirt to escape slowly before agitation engages.
What happens in all BD and DD agitators is that air builds up under them during fill. The Roto-Swirl and Penta-Swirl have cavernous spaces underneath that don't blend well with floodable bearings and centerposts. When agitation begins, a massive bubble of air escapes, and the machine appears to BURP. If the seals in the machine are really bad, the air will escape as the machine is filling. When the air comes out, it is displaced by a flood of water into the centerpost area. If the seals are weak, more water is going to rush in than would otherwise.
The Roto-Swirl was modified in 1978 to have more of tubular center to account for some of this, but nothing beats the Penta-Vane and Dual Action that are slim and trim in the center where air can't hide in the first place. The White Penta-Vanes have the above mentioned weap hole too. I hate to suggest it, but I think that Roto-Swirl, especially coupled with a large capacity basket (and therefore more downward pressure on the seals with all that extra water on the outside) should not be used in that machine.
Finally, it does sound like you have water in the transmission, and it may not be recent if the oil is already gray or brownish. If you tip the machine forward, water may pour out of the transmission vent hole. There are ways to shore-up the transmission by replacing the shaft seal under the trans cover. I have had machines that leaked several cups of clear water when the trans was tipped, and others that had blended with oil to make a chocolate milk goo that looks just like automotive oil after a blown head gasket.
I experimented in 1995 with a particular nasty transmission by cleaning the entire unit piece by piece in a parts washer, and putting it all back together with new seals. It has done thousands of loads for me since and I still have it, but you're talking the most in-depth rebuild one can do on a belt-drive.
Make sure whatever you do with your machine, that the top of the agitator is properly sealed on ANY short centerpost model. If you insist on keeping the Roto-swirl, make sure you use the 1978 and later agitator cap, stud and seal. The pre-78 are NOT sufficient in any way on short post machines. The short post machines are great because they eliminate nearly 100% of the bearing wear that so badly plagues the older tall and super-tall post machines, but this is exchanged for self-destruction when the seals go bad.
A lot of folks who used to rebuild these machines are going to tell you that the machine is 'toast' in it's present state. It will be a lot of work to properly fix, but once or if you do, it will be good to go for a long time!
Gordon
