Things may be different in the UK but in oz there are 2 types of LPG.
Propane used as domestic and camping fuel. Generally has the evaporation occuring in the bottle with the heat supplied by the environment. At high usage rates (industrial WAY outside intended) water condenses from the atmosphere and forms an insulating blanket of ice on the bottle hence gas supply tails off.
Propane/Butane mix (plus anything else of low BP from the cat cracker) used for vehicle fuel. Vaporization in the tank is only to provide pressure for delivery of liquid to a vaporizer with heat supplied by the engine coolant, Not to be used for domestic/camping use as there would be a variation in the mixture strength with the propane coming off first.
LPG works fine for car use (12 years, 240,000K including a fair bit of snow work) can't see why it couldn't be used for a/c with an appropriate vaporizer. The tank weight could be addressed with filament wound kevlar as for oxy bottles.