Ordered the Suspension Rod Kit, and (2) sets of the tub centering springs (my machine only had two originally). The video was clear and easy to follow, and happened to show a very similar appliance to my own (a Kenmore 110.20022012).
Upon removal, the old suspension rods did not appear to be damaged, and I could not detect much of a difference in spring strength between old and new, but replacing them seems to have completely solved my "gorilla in the washing machine" issue.
This was a very satisfying repair experience, and I hope it has extended the life of my washer for several more years.