I have transported propane tanks on their side as well.. HOWEVER, the other poster was correct, the tank is designed to always be upright, Full time upright. Due to the way the relief valve works.
If the tank heats up (Say due to sunlight) you do not want to vent liquid propane, first, it is way more expensive to vent a gallon of liquid than it is a gallon of gas, and 2nd, it's way more explosive as well. Odds of gas (vapor) venting fast enough to build up an explosive concentration very low from a single tank or even two tanks.
Liquid however can do it.
True story:
Instructor: What happens if you mix Propane and air in the right ratio and add a spark.
My answer; You land 2 counties over
Instructor: Correct (once the laughter died).