An average 3-4kW chimney uses only about 500L of gas per hour. That are really low volumes, even for 1/2" pipe.

Joule Thompson effects are measurable over an orifice i.e. Regulator but not really in these cyllinders. Also with these low pressures 1-2bar JT effect would be +-1 degree Celsius for pressure drop to atmosphere entering the chimney. Yes, the tank can hold more heat as more fluid is present but will still quickly cool down/warm up with the ambient temperature.

I dont think OP has any benefit with a bigger tank looking at his consumption or other circumstances.

Wait what? The volume does not matter for pressure. For propane/butane tanks only the temperature is of importance as they liquefy on lower temperatures and the pressure decreases. Also pressure drop in tubing/piping is neglible in low flow short run conditions. Smaller tanks do run empty quicker though.

https://www.engineeringtoolbox.com/propane-butane-mix-d_1043.html