Based on searching the web, it seemed as the problem of my washer overflowing was due to the water level switch. So, I replaced it and the tubing but it didn’t help at all. A few other things are going on. On the regular cycle, if I stop the water filling by pushing the dial in and moving it past the water fill stage, I can hear a slight buzzing noise but the washer never starts to agitate. Also, I have the water temp set to Warm/Cold but when I switch it to Warm/Warm (on the fill cycle), the volume of water increase greatly as if it was previously on the Hot/Cold setting (water was hot). I did manage to get it to agitate on the Heavy Duty cycle by moving the dial past the fill cycle all the way around several times.
I assume you also made sure the tube to the water level switch was clear, but if not be sure and check it.
However your problem sounds like a timer issue, that the timer is not processing the stop command when the washer is full and the water level switch closes.
Try replacing the timer, and if you buy a timer from this site and that does not fix things you can return it.