Here is what I did when I had to ship a rocket cross-country. It doesnt use 2x4s (you can definitely get away with something smaller), but is still similar to to your idea.
The bottom plywood plate unscrews and the slot near the nosecone base in the picture is where the nosecone U-bolt inserts and the cone is held tight against the hole in the center cut out. The 4" diameter body is held in place by the wood square on the bottom plate. There is a similar assembly on the top that holds the other side of the body tube. The entire wood assembly fits in a cardboard box. I put tape wherever the rocket contacts the wood so the paint doesn't get messed up.
NAR #89512 L2