This information is amazing! I have one of these washers with the same fault, except it also has a broken belt and the base of the timer won't turn with the handle part of the knob (you can hold the base and turn it that way, so I assume something is stripped). I think the broken belt may be related to the shift coil failure, causing overload on the belt.
So, how about replacing the thermal fuse with a self resetting thermal overload? I have less experience than many of you, but I've seen self resetting thermal overload protectors in a clothes iron and a bottle warmer. Has anyone replaced the thermal fuse with a self resetting thermal breaker? Is there room inside this thing for that? I haven't yet taken mine apart.