"However, in an inverted canister stove, the fuel is still liquid when it leaves the canister. The phase change happens at the burner (i.e. in the pre-heat loop). The fuel expands some 200+ times its original volume when it goes from liquid to vapor. A 200 fold expansion gives you a lot of pressure at the burner even if your canister has a fairly low temperature"
Think about this for a moment. The liquid fuel is boiling in the pre-heat tube and therefore there is a ~200x increase in volume. That volume wants to go somewhere - where? The fuel line has restrictions at both ends - the jet at one end and the valve at the other. So, if the boiling fuel in the pre-heat tube were to increase the pressure in the fuel line, that increase in pressure would be evident at both ends of the fuel line - the jet and the valve. That would create a 'back pressure' at the valve, forcing fuel back into the canister. Obviously that can't happen!
So, what does happen? The highest pressure in the system is in the canister. After passing thru' the valve, the pressure in the fuel line is lower. And after passing thru' the jet the pressure in the burner tube is lower still (lower than atmospheric, that's why air gets sucked in thru' those air holes). The boiling fuel in the pre-heat tube does not increase the pressure in the fuel line at all.
"But", you say, "when I invert the canister I see the flame increase, so there must be more pressure!"
Yes there is, but for a different reason. The fuel valve is restricting the flow of fuel, but it is restricting the (approximate) volume flow rate, not the mass flow rate. So, if a particular valve position and canister presure were to give say 1ml per minute of fuel, then with the canister upright that will be 1ml per minute of gas, but with the canister inverted what will be 1ml per minute of liquid, or would be if there was no jet - there is not enough pressure to force 200ml per minute of gas (from the expanded liquid) thru the jet. Nonetheless, when the canister is inverted there is an increase in the mass flow rate of fuel and so a bigger flame.