Odd that the in-line shut-off didn't work. Must be faulty. They are designed to be able to turn the shower on and off without messing with the temperature adjustment.
Generally how a diverter works is the piping to the shower is always open and simply choking off the tub spout creates enough pressure for the water to overcome gravity and take the alternate route. There could be some constriction in the tub spout or the diverter is not full open. I would start by removing the tub spout and see how well it flows out the stub pipe.
I wonder if someone didn't install the rough-in valve body upside down. Often, the shower outlet will have a smaller port than the tub spout outlet.