Kohler K-304 to K-306

We have a Kohler k-304 shower valve and our supply pipes are 1/2 cu. The flow rate is sooo low that the valve can't be in the cold/warm temp range or else the spout diverter will release back to the spout...Are there any tricks on this valve to increase the pressure...hidden restrictors etc.? If not then we'll have to swap out the valve with the Hi Flow k-306. BUT then again will the k306 with only 1/2 cu supply still increase the flow? Thanks for your opinons. Tony

Do you have low pressure other places?
The last home with this symptom had a very old pressure reducing valve that had gone bad.
I replaced the PRV and the diverter started working.

Your problem is NOT with the water supply lines. You might have the same problem a plumber friend ran into a couple of months ago. That Kohler valve would not flow at all even after he rebuilt it. The problem was, and this gets tricky to describe, in the sealed opening for the tub spout. Material had accumulated in it until it plugged the flow back up to the shower riser. I had to remove the threaded cap, (which of course they had soldered on to be sure it would not leak), then fabricate a "U" shaped wire to insert into the opening an reach up to the opening in the valve body where the water was supposed to flow out. If the valve had been installed upside down, like I usually do for shower only installations, it would not have happened.