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Have you tried these diagrams to get to the transmission?
I'm guessing that you have examined the coupler and it was in good condition.
On the diagram -
part #17 holds the outer drum.
This usually ends with a not spin issue and is commonly repaired by replacing the "wig wag" yes... Whirlpool's common name for it.
The remedy is to replace the "wig wag"
The best way to do this is take the hoses off the washer, and pull the drain hose out of the drain, and lay the washer on its front. Then take the 2 5/16 screws out of the back panel, and you will see the wig wag.
Take the 5/16 screw, that holds it in place out, and then you most likely will have to hit hit up to get it off. Do not hit the shaft.
Once you have it off, clean up the shaft, and then put a little dishwashing soap on the shaft, so it will slide on a little easier, and then line up the two plungers, and the center shaft, at the same time.
Put the screw back in, and wire it back up, and give it a go.