Actually, the combination of turning the propane on slowly AND not having any propane appliances on provides the solution. Here is the detailed, more technical explanation from the RV Doctor, Gary Bunzer. 

"Let’s talk about a couple of safety features on these new pigtails. Both features are parts of the big green nut.

The first is a black thermal-sensitive bushing found just behind the green nut. If this bushing is ever in a fire with temperatures between 240°F and 300°F, it melts and allows the brass nipple inside the nut to move back about ¼ inch, which closes a small piston inside the cylinder valve totally shutting off the flow of propane. This innovative feature will help prevent fires or explosions.

The second new safety feature is called a “flow-limiting-device.” Its purpose is to restrict the flow of escaping gas if there is an excessive leak in the RV propane system. This second “flow-limiting-device” feature and how it works forms the core of the secret! Almost every time the cylinder valve is opened, a small ball in the center of the brass nipple (inside the green nut) is pushed forward into a brass seat. This seat doesn’t totally shut off the gas. By design, it allows a small amount of gas (by-pass flow) to go into the RV propane system. If everything in the propane system is closed and in the off position and there are no leaks, the by-pass flow builds up a back pressure. This equalizes the pressure in the ball back of the seat and allows unrestricted flow through the system. All this happens in about five seconds and the user doesn’t know it’s happening, appliances light, furnaces and water heaters run as normal.

Now lets look at the same system but with the oven control left in the pilot on position. Again the cylinder valve is opened, the ball is pushed into the seat, the by-pass flow goes through the system but this time it can’t equalize because the flow continues out through the open oven pilot. The user goes inside and starts cooking dinner. Two burners on the range top are lit and everything seems okay until the furnace comes on. At that point, the flames on the range top are drawn down and the furnace won’t ignite, everything seems starved out. The reason? We don’t have full-unrestricted cylinder flow to run our system, we only have the small by-pass flow which is far too small to feed the appliances trying to operate.

HOW TO FIX THE SITUATION: Turn off all the appliances, turn everything to the closed and off position, wait about 15 seconds. If the system is closed and tight, the back pressure builds up, equalizes and feeds unrestricted cylinder flow to the regulator for normal operation."

And if you still have problems with propane, consider replacing the pigtails with the big green nuts with pigtails that have a big red nut (fairly new, but they are approved for RV use and allow double the output) as this may help your propane flow issues, especially if you have propane cylinders on opposite sides of the rig.