No, don't blame the parts. As Gary's diagram shows, that's actually the starter RELAY. A solenoid would be ON the starter, but the solenoid style of starter wasn't used on Ford gas trucks until '92. Is it loose on the bellhousing? Is its rear face parallel to & hard against the shim plate between the block & bellhousing?
Everything is tight and lined up correctly, still doing the exact same thing. I suppose next I will turn the engine over manually this weekend and see if there is any missing teeth on the flexwheel. And if there is...I suppose I'll be pulling a tranny. Never done that before!