Replaced the shaft and bearings. It truly is a difficult job, and mine was a nightmare because the lower bearing came apart instead of coming out. I had to cut a piece out of the shell with a Dremel to get it out.
I recommend:
1) Watch the video before tackling the job. Watch it again as you work.
2) If you can't round up a helper who has changed bearings before, I recommend replacing the entire tub. It is about $300 more but is much less risky on an older machine.
3) Allow three days to do the bearing job. The adhesive on the seal has to cure overnight and it is a big job if the machine is more than a few years old. Tub replacement should be a same day thing.
4) Live chat with the parts support was crucial - it turns out Kenmore parts can't be reliability checked in the compatibility checker.
5) Wash out any dirt in the tub before reinstalling the basket. This sort of machine works by recirculating the water in the tub.
6) The required tool is required.
I spent about 8 hours on this 9 year old machine that has had a lot of hard use. Newer machines, especially without the leakage, should have fewer disassembly problems. Assembly is not hard.