ok, a few things.
body grounds suck, everyone agrees.
The caspers adapter has a ground wire (a pair actually) that you are supposed to ground to the dashboard. I never liked that. I'm not saying this is an issue, but just unbolt it and see if anything changes. You could extend the wiring and ground it to the engine.
On the battery vs engine grounds. everything in the car is grounded to the engine, running some grounds to the battery would create loops. Not a step in the right direction. But you could try it and see if it changes the symptom.
what kind of shape is your negative battery cable in? tight to the engine?
Bob