It seems to me that it boils down to the basics... you have a certain volume of water at a certain pressure. If the diverter is fully open, and there is more water coming through than it can handle, then there is overflow going to the shower.
The water pressure can't be more than what is available coming in, so that should be regulated for the whole house; if it's too high, valves could fail elsewhere. If it's correct, then this can't really be the problem (directly).
So, it must be a matter of pipe sizes or diverter valve capacity. There must either be an obstruction at or after the diverter valve, or the pipe going to the shower is too small and fills up, so to speak. If the pipe going to the shower head was bigger, it would act as a reservoir and take more water before it overflows out the shower head.
It may be that there is simply too much water coming to the shower, and a flow restrictor leading to the valves, or limiter on the valves is needed. I don't know if the valves have a way to limit the water. The main question would be whether there is lots of water coming out of both the shower head and the tub outlet when the valve is at the setting that does not come out of the shower head when it shouldn't.
Sorry this isn't exactly a full answer, but it's too much to put in a comment, and I thought it might be helpful for troubleshooting the problem.