The machinist in me wants to add a thought about this.
As anyone who has work on this knows - the shaft has two machined surfaces, and in between them is an unmachined area. That unmachined area in between is what tends to corrode, or at least that was the case on our machine.
Rust tends to expand material and that expansion hangs up when you try and lift the basket off. The basket surfaces which ride on the shaft are, I believe, merely plastic. So one possible gotcha in this is those surfaces will be damaged when you lift the basket off. There really is no avoiding that. If you lift the basket straight off with a puller tool, then the plastic bushing surface should only be scratched in a longitudinal direction. Of course that assumes the person doing the work does not allow the basket to rotate while using the puller tool. In most videos not much care is taken in that regard.. hint, hint.
If you use the Agitate test cycle method, there is some risk that the rotation will score the surface over a larger area.
After I removed the basket I carefully cleaned the plastic surfaces of residual rust, etc, with a toothbrush and paper towels. I did not see any significant scoring, etc. Everything was greased and it is working fine and dandy.
I read a post where someone suggested that vinegar, and five minutes time, allowed him to pull the basket off. Apparently that dissolved the rust or mineral deposits. On our machine it was more like rust and not mineral deposites. I tried the vinegar approach but it did not work (it may have even gotten a bit worse, as the vinegar can disloge some particles and create wedging). I think once you use vinegar you are committed to removing the basket in order to clean the vinegar out. You don't want to leave that in there.
Anyway, however you do it, good luck wrasslin those baskets!