You are exactly right. Bone dry dirt won't pack.
If you are using coil springs which are swiveled on the bottom, the hole for the trap needs to be shaped like a small bowl. This allows the swivel a place to go so it doesnt bottom out and the frame rests on the outside of the bowl.
If you are using rebar stakes with washers, you can drive the stake in a place which allows you to use it to rest the loose jaw of the trap. It rests over the washer and against the stake.
Just a couple of things which might help.
Randy