I had poor cold water pressure in the shower. Full pressure everywhere else. Removed valve bodies, saw broken and dried rubber gaskets.

So, I replaced both hot & cold American Standard 2 handle valve bodies. New valve seats.
I proved water pressure OK, I think, by means of water squirting out without any valve body.

Now, the cold pressure seems only slightly better. Furthermore, the point of desired temperature is hard to hit: 100% hot, 30% cold. 29% cold too hot, 31% cold too cold. Why such a fine tolerance on a new valve?

Can I replace with pressure balancing system without major tile destruction (It's old and hard to match)?

Can I do anything to diagnose the problem? I live for a decent shower.

With a two handle system I don't think you have a pressure balancing system at all. A single handle system balances the two but not what you have. Try 100% hot, zero cold and observe or measure the volume. Now try zero hot and 100% cold and observe again. They should be pretty much identical, if not disassemble those valves again and look for more debris or anything not tight like the washer screw or the valve seat.