The problem getting the basket drive off...
Paul,
What you are describing happens from time to time, in fact I had it with my 1986 KM 70, which isn't a high-mileage machine. There is a sleeve bearing inside the spin tube which rides against the agitator shaft, toward the top of the tube, just below the area where the spin tube seal is installed.
With use, the spin tube seal will cause some friction wear to occur on the agitator shaft, usually as polish marks (when you're lucky) and later as small grooves or gouges on the agitator shaft, just like the bearing seals can do to the outside of the spin tube. If or when these grooves/gouges get moist, the worn bare metal of the shaft starts to rust, and expand. It then won't allow the bearing in the spin tube to pass by when trying to remove the spin tube/basket drive.
Sometimes these can be very difficult. I have always been able to separate the parts, but a few have taken serious effort. My personal method: Make sure the drive pulley is secure on the gearcase, because you'll need it as a gripping surface and to prevent the internal gearcase parts from moving. Then clean the spin tube so it is not slippery in the center and you can get a firm grip on it. **Be sure the gearcase is engaged in agitate**. Grab the drive pulley with one hand, and the spin tube with the other, and TURN the spin tube back and forth while pulling UP on it, and hold the drive pulley steady so the agitator shaft doesn't move. Twisting it with upward force will eventually raise the tube over the wear-groove in the shaft. Adding some turbine oil inside the worn area may help keep things moving.
If a great deal of effort is required to make the above work, it can leave the sleeve bearing in the spin tube damaged, but if you don't plan to re-use the spin tube, it doesn't matter.
This is a method I started using on my own and has always worked for me, but it can be tedious - perhaps the professional service guys of AW know a better way?
Gordon