Hmmm...
Tom,
Based on the age of the machine, I would check the cooling fan on the motor which will often break and spin independently until it catches up with the motor speed. It will often screech at first and then stop making noise. Since the pump runs only in one direction on your unit and generally runs continuously until it stops for the final rinse, it can remain fairly quiet once the machine is started. But it will screech again when restarting for the last rinse.
You can check this by watching the motor from underneath when it starts up or you can turn off all the power and reach in and try turning the fan with your finger. Sadly, you cannot get the fan by itself so you will have to replace the motor or get anoter motor with a viable fan on it. Let me know what you find. I just found a box of motors and will check the fans on them. Most of them are in good shape.