Ok. The chain was not fed properly through the RD cage. Specifically, it was going below the little cross brace between the jockey wheels, when it should have gone above it. So it was rubbing that and causing the rattle/ratchet. That explains why it was louder on the big ring, the higher chain tension made it more pronounced.

The interesting thing is that I had a couple hundred miles on the chain, but only became aware of the noise on the most recent ride.

I tried to get the chain over into the correct position without breaking it, but that was not possible.

I broke the chain and reused the pin, which is allegedly a no-no with modern Shimano chains, but it seems to work fine.