I would think that if you are reversing the sprocket and chainring, that you could start a brand new phase relationship using either set of links, since you are basically starting with a fresh gear set. My understanding is the chain rollers only contact one side of the tooth, and flipping your rings around will make the chain contact the unworn surfaces. I'd guess that you are hearing a chain that was worn a bit too long, and now it is aggressively trying to dig a comfortable pattern out of your rings to match the brand new chain pitch.
Is your bike equipped with sliding dropouts or an eccentric? Mine has a chain tensioner, so I have to follow the basic rules that apply to deraileurs when it comes to chain wear and replacement. But if I had a sliding drop or EBB, I would just wear the chain and sprockets out together in a phase relationship. Seems like alot of folks are getting 10K+ miles when doing it this way. Assuming you have the adjustment range to keep the chain tensioned.
Now for my question: For those with a bike equipped with sliding drops or an EBB: Say you run a chain, sprocket and chainring together in a phase relationship until it is worn so much that you can't compensate for the chain growth and it is now time to change the chain. Can you fit a new chain, then change the phase relationship by one tooth instead of flipping the chainwheel and sprocket?