Transmission Schematic
Ken, Attached is a diagram of how your transmission works. This is not your specific transmission, but yours is made and functions the same way. The cone clutches inside are what transmit the power to the output shaft. Basically a male bronze cone which pushes into a steel female cone which is machined onto the backside of the gear. In a nutshell, you depend on the friction in the cone clutches to transmit the engine power. Putting something like STP may increase the slippery-ness enough to cause the cones to slip .. that would overheat the cones and cause some problems which would eventually fail the transmission. I wouldn't do it.. as others have said, use straight grade 30 motor oil in it ..
When the engine is running, all the gears are spinning .. in neutral, the output gears are spinning on the stationary output shaft..The shift cone is stationary. When you put it into "Forward" the drive cone moves into the recess of the left side gear and begins to slip slightly as it contacts the gear; the spiral thread under the cone pushes the moving cone harder into the gear cone until it does not slip. The gear and the cone are then turning at the same speed, driving the output shaft..
You can see from the right hand drawing of the drive cone that it has grooves .. Those grooves are designed to channel the oil away from the contacting surfaces so that they don't slip while driving.. heavier oil or oil with more "slickity" may not let the cones lock together properly..