Today I think I finally figured out why the Milwaukee regulator behaves as it does. When I first set up the newly filled tank of CO2, I set the regulator to about 20 psi, set the bubble rate, and come back to look at it after a half hour or so - the regulator is putting out just above zero pressure. So, I tighten the knob some more to get back to 20 psi, come back in a half hour and the regulator is back to near zero. After a day of this, the second day the regulator stays where I set it and the bubble rate is therefore constant.
Then, as the liquid CO2 runs out, the bubble rate goes up a great deal. I loosen the knob until the bubble rate is back where I want it. But, it is soon back too high.
Both of these quirks can be explained if you accept that that regulator, at any given tightness of the adjustment knob, produces a pressure that is highest when the tank pressure is lowest, and lowest when the tank pressure is highest.
A newly filled tank is very cold, and stays that way for hours. So, the tank pressure is around 500 or so psi, not 700 as it "should" be. That low tank pressure means the output pressure is high. As the tank CO2 warms up, the pressure in the tank increases, and the output pressure drops. When it finally reaches room temperature the tank pressure is about 700 psi, and the output pressure stays at whatever it is set at.
But, when the liquid CO2 is used up, the tank pressure begins to drop. That means the output pressure rises, increasing the bubble rate. This rising of the output pressure continues until the tank is empty. This is the cause of "end of tank dump".
There is only one "solution" to this: let the newly filled CO2 tank sit until it warms up to room temperature, before connecting it to the regulator. Then, as soon as you see the tank pressure start to drop, disconnect the regulator and get a refill of CO2. I just live with the problem, knowing I have to readjust the output pressure every half hour for a few hours after I hook up the newly filled tank. And, I start backing off on the adjustment knob as soon as I notice that the tank pressure has dropped from 700 psi.