Yes, I replaced the load sensing switch (W10292584, replacement for W10177795) and the timer (W10177827).
Other forums I’d read across the web pointed to the load sensing switch first, then the timer second. I have replaced both and the machine’s behavior has not changed; it still only operates in "Extra Rinse" cycle.
Some posts have suggested the lid switch, but when the machine is running in the "Extra Rinse" cycle and the lid is opening, the lid switch shuts down the machine as intended.
I have similar problem with my whirlpool washer, it operates in extrarinse only, does not operate in other cycle modes, it just spins in other cycle modes.