Not quite what I said/meant Rob..
There's obviously air in the tank on the first fill, air above the liquid gas might compress to higher pressure (due to rising liquid gas level when you fill) than *would-be* gas vapour pressure in the tank if the tank didn't contain air. E.g. if remaining tank headroom after filling with gas is only 1/10th total tank volume then there will be 9bar of air pressure in the tank because we compressed the air above the liquid gas. But if the tank didn't contain any air the pressure in the tank would be solely and directly related to the gas pressure, which would only depend on it's temperature.
Obviously gas wouldn't flow from a pump that is only pushing 7 bar into a tank that has 9 bar pressure and this is irrespective of if the tank's pressure is due to compressed air or gas pressure. It seems some pumps output (pumping) pressure is related to temperature because where pumps have a pressure gauge they seem to push lower pressure when it's cold (weather or perhaps liquid gas temp in bulk storage tanks at forecourts) conditions than in warm conditions. Perhaps these pumps push at pressure that is relative to their input pressure, the input pressure would just be pressure of the bulk storage tank at the forecourt which is (again) solely dependent on temperature of the gas in the bulk storage tanks.
In cold weather propane pressure in a vehicle tank can be low enough for compressed air to be the limiting factor preventing further filling when pumping pressure is low.
To get rid of air in the tank, filling to half full and running til low then refilling wouldn't work. There's only one way for air to come out of the tank and that is by being pushed through the tank outlet toward the reducer but since the fuel pickup pipe is usually submerged in liquid gas that won't happen until the tank is completely empty of liquid gas. Getting rid of air out of the tank this way (pushed toward reducer) can happen much quicker on a mixer system, which is more likely to allow the engine to run at least at low load while there is just vapour in the tank, than on a sequential system where at least in part due to the higher reducer output pressure the reducer and rest of system won't allow the engine to run when there is just vapour in the tank.
Even with a sequential system some vapour containing air will be forced toward the reducer each time the tank is run to empty but it could take running the tank to empty many times for enough air to be pushed toward the reducer with a sequential system to make much difference to the amount of air in the tank.
To speed up the process of getting air out of the tank it should be possible to: Before fitting the tank put a few litres of gas in it, turn it upside down to get the pickup tube into vapour rather than liquid, open the outlet, air will come out with the gas vapour. On some installs this isn't possible (might need to fit the valve after fitting the tank) and (in any case) an easy way of getting at least some air out of the tank would be to fit the valve and tank, use as normal for the first tank full, when it is empty disconnect the pipe from tank outlet, open the tank solenoid to allow remaining gas in the tank push some air out... there will always be some pressure in the tank even when it's run empty. If you did this multiple times you'd get most of the air out but once or twice might be enough to prevent air pressure having an effect on fill level and speed even in winter
In winter weather tank pressure might only be 4 bar, in hot summer periods it might be 10 bar... This is Irrespective of how full the tank is as long as the tank contains some liquid and isn't filled to 100%. But 'irrespective' isn't true if the tank also contains air which is compressed (above the liquid gas in the tank) to the point that the compressed air is at higher pressure than tank pressure would be without the air in the tank.
One proviso in all of this - It all depends on the pump pressure, so is the pressure on pump gauges (where fitted) absolute pump pressure or do the pump pressure gauges reflect the pumping pressure above tank pressure. All of the above depends on the gauges showing absolute pressure. Since fill speed seems to slow as a tank fills (and since tank pressure is only effected by temperature unless it contains air) I do expect the pump gauges to show absolute pressure (well not strictly absolute but you know what I mean, relative to atmospheric pressure).