Just curious. You say the pressure is reduced. Is it reduced for all temperature ranges, or just for say the hot end of the spectrum? I know that in our cold climate, where street water comes in frigid, the pressure in the hot water end of the spectrum is moderately lower than just getting a full blast of cold water.

If you have separate shutoffs for the shower are they both open all the way? I doubt if that is the problem but it probably doesn't hurt to check. Do you have a bath and shower fixture or just a shower head?

I think you will find the difference in volume is a result of legislation and regardless of what type of shower mixer you install you would still have the same result.

In the 50's showers had as much as 5gpm but due to current regulations showers are now limited to 2.5gpm.

We have separate hot and cold now in all three bathrooms (house built in the 60's) and when we replaced them in the kids' bathroom with a single handle the water pressure was reduced. I asked my plumber and he said it was because of the mixing feature of the new fixture. We are doing a bathroom "refresh" of my husband's bathroom and he is adamant about keeping the water pressure. So we are not replacing the double handles at all. The problem for you is that I doubt you can go backwards. According to my plumber, all new fixtures have to have a single mixer. The only thing I don't understand about that is that I see hot and cold handles advertised all the time online...

My understanding is that pressure balanced tend to reduce flow. I did a 3/4 inch thermostatic and it flows like 17 gpm so it will not reduce flow. I would think that they make pressure balanced that will flow higher - it is just a matter of checking specs. And going with 3/4 inch even though you don't really need that much flow.

All is certainly not hopeless and you don't have to stick with 2 controls to have pressure - that is patently ridiculous.