I'm not transporting long distance, just from my home to the dealer for a fill up and then back home to put back on the trailer.... but I just lay the tank on it's side. I use a doggie bed and the tank rests right in it, no problem. I just lay it on the back seat (car or truck) and it doesn't move. But there again, it's only like that for about 8 miles one way.
In my previous camper, I build a cradle and keep an extra 20 pound tank I used for our Coleman Camp Stoves in the pass through. Here again, it laid on it's side, but the entire 8 years we had that trailer, it never leaked, it never moved, and unless filling the tank or using it with the stoves, it was stored all the time in this manner.
I once posted a photo of how I did it (several years ago), and got bashed to death for laying it on its side. But I never had any problems transporting this way in the 8 years.
With our current trailer ... we have a built in outside stove that attaches to the trailer propane plumbing, so we don't carry the extra tank any more. In fact we don't even have it any more, or the Coleman Stoves.
Here's the bottom line .... if you are transporting propane tanks and cylinders for pay, then they have to be upright, safeguarded, secured, strapped down. But if you are transporting privately, just use your best common sense! Keep them from moving, and if in an accident, have them secured in a fashion they don't become flying missiles!
I'll probably get ripped to shreds with my response, but that's OK. It's happened before.
Use your common sense. You'll be OK.