Hi chopsuwe,
You describe a very interesting problem.
You say the Cold pressure is much lower than the Hot pressure, at your shower wall outlet.
Do you have a two level house - is the shower upstairs and the HWC etc downstairs?
I can only think of two possible explanations so far, but if you give us more info about the levels and distances, that might help.
Anyway, if the shower is upstairs but the Cylinder and Pressure Regulator valve are downstairs, my guess is the Pressure is set (has dropped) too low. The valve may be old, and the spring has got tired. The explanation - cold water is heavier than hot water, so is harder to push uphill. If both hot and cold feeds to the shower come from the same regulator valve, then the regulator pressure must be only just over what is required to get the cold water there. I would suggest the pressure needs to be increased a fraction, but what's the setup first?
Is the Hot Water cylinder Open Vented? Is there a vent pipe running from the top of the cylinder up through the roof? If not, best not play with it...
The only other explanation I can think of for this strange behaviour is that there is some weird plumbing between the cylinder and the shower, and that for some reason, the cold line has developed an "air lock" - or at least, a partial one. For that to happen, part of the cold water pipe to the shower needs to run back downhill on its way up. Then, air can get trapped in the downhill section, and cause this kind of pressure reduction without completely stopping the flow. Seems unlikely that it would last for months on end, but strange things do happen. But I'd suspect the pressure valve first.
But, just for fun: Do you know if any other cold taps are fed from the Pressure Regulator valve? If so, you could try this. Turn off the Cold water supply to the Pressure Regulator. Turn on the Shower, to Max Cold. Find the lowest (in height from the ground) Low Pressure cold water tap in your house. Turn that full on and let all the water run out. (If the water doesn't stop, it's not a Low Pressure tap...) If it's low pressure, once the water has run out, close that tap, then turn the Cold supply to the Pressure Reg on again. Let the cold water to the shower run for a couple of minutes. You may get some air bubbles etc coming out.
See if that helps. If not, I'd say the Pressure is too low...
I note that you said that the plumber you asked only said "could" cost $400. Because he doesn't yet know what's wrong, and maybe he's thinking a new pressure valve, plus time to fit etc... Just to give you an idea of what you might be in for. Sounds okay to me.