I have used an additive to the oil which does not seem to have made a diff.
Kill-a-car in a bottle. Merely masks the problem rather than fixing it. Think of it this way..oil is a lubricant for your engine, but you're adding something to the lubricant that's made to do this exact opposite of lubricate.
Does it sound like ticking/knocking, clacking, or metal chatter?
Coming from towards the front of the engine or towards the valve covers? Sound like it's worse on one side of the engine vs. the other side?
You could try taking a 3/8 extension and setting it on top of the valve covers while the engine is running and see if the sound gets more noticable or if you can feel added vibration through the extension on one side vs the other..
If you take the oil cap off while the engine is running, does the sound get louder or stay the same?
Our 3.7 engines are extremely notorious for having a noisy valvetrain, especially when being cold.. but they're also notorious for throwing rocker arms, stuck lash adjusters, and dropping valve seats.. but if either of these happened, your noise would either be much more evident, or your engine would have no compression in whichever cylinder the valve seat dropped out of.
No check engine light I imagine, or you'd likely have stated so.. But a thrown rocker arm, or stuck hydraulic lash adjuster often won't even thrown a MIL.