Everyone has different comfort levels of how they pack their plane and what to take apart to move on a truck. I have not moved a flying airplane, but have moved the complete airframe with engine of my 9A from Colorado to Idaho, back to Colorado, then back to Idaho again. I hope that is the last time!
I have a 7'x16' two axel auto hauler. I took the engine off and took it off of the gear. I built a platform as wide as the trailer tall enough to put the wings and entire empennage in. I spanned the 7' with 2x4's at 20" oc with 3/4" plywood as the top. I then put the fuselage on top of the plywood platform. I started with the engine in the back on the deck of the trailer, but it put the CG on the trailer too far back. I built a plywood box and put the engine on the side of the fuselage over the two axels. I put a 1x6 through the wing channel and fastened it down with blocks. The engine mount makes a good tie down point but there isn't much in the back. My fuselage started as a tail dragger so I had the hardware in the back to use to tie that down.
I was able to get my entire plane, engine, compressor, and most of the tools on my trailer and it rode pretty well. I was able to do the 80mph speed limits in Utah and Idaho without too much problems.
As a disclaimer, I have been in construction my entire life and have hauled about everything used in construction. You need to understand how to tie things down, use blocks to keep things from shifting, and know how to load the trailer so you don't fishtail all over the place.
The other thing you need to do is call Kathy or Jenny and get insurance! That is a MUST before you or anyone else hauls your plane anywhere.