There shouldn't be a pressure problem at the tank, large or small. The tanks have to pressurized to the point that the propane is compressed to a liquid state. As the propane is used, the liquid boils to replace the lost vapor in the tanks. The regulator reduces the higher tank pressure to the lower pressure needed at the appliances.
It's been a long time since my physics classes but I think the pressure in the tanks always has to be at propanes vapor pressure, the pressure at which the liquid changes to gas.