So, the noise is present initially on cold start, goes away once the idle drops, but then is still present under acceleration and load at low speeds (and probably at high speeds but I can't hear it anymore).
Definitely sounds like a rattle or just something loose. I looked underneath and didn't see anything obvious. It does seem to be coming from the valve area or the muffler canister right near it, but it is hard to tell.
I have tried the different exhaust modes and can hear a difference, so I think the valve is doing something.