The vapor pressure of propane depends on the temperature of the tank. Here's a chart:
Data lifted from Engineering Toolbox
The 375 lb figure for the relief valve is not the pressure of the propane. The operating pressure of the valve is based upon the design MAWP (Max. allowable working pressure) of the tank, derated by an adequate safety factor. I haven't taken the trouble to look up CGA specs for portable propane tanks to determine the derating factor.
As said previously, you should extend the line after the regulator. It's a lot more forgiving of construction mistakes.