That pretty much explains why Frigidaire techs keep
both boards on their trucks

Why not be practical in your approach rather than use the shotgun method? (even though any parts you order thru these links can be returned without question). Before you wen't off on Frigidaire there, you forgot to mention what the washer was not doing besides the vague E5E code, so lets
assume it won't spin.
In the field, I have learned to place my voltmeter leads at the motor speed board itself where the black and white wires send it power from the main control. If, during the spin cycle, you do not detect 120 volts at these 2 wires, the main board is likely bad or a wire is broken on it somewhere. If there IS power down there and nothing spins, you have a bad speed control. Does this clarify things some?
btw, I read today where Frigidaire (Electrolux) is closing their mfg plant in Iowa this year, leaving 600 more folks without jobs here. Somewhere in Mexico, 600 families are getting them.