The OP's comment about shifting having a temporary affect reminds me of something I had on my tourer.

Does the bike have a freewheel versus a freehub/cassette? If so, there may be friction and failure of the internal freewheel mechanism. The outer cogs aren't seating properly on the inner body of the freewheel. The result is an intermittent clicking or clunking as the pedals apply forward force to the chain. Changing the gear ratio changes the clunking slightly as more or less pressure is applied. This noise would come up every 30 miles or so, then would fade away.

Anyhow. I solved it by first injecting a light solvent (WD-40) into the freewheel (removed from the wheel, but you could do it on the wheel, keeping the freewheel level and facing upright.) I spun the freewheel until I could detect no more sense of grinding or grit. Then I began to pour a heavier (30W synthetic) motor oil into the central portion, allowing it to soak into the freewheel). Wearing nitrile gloves, I picked up the freewheel and spun it for a few minutes again, and re-applied motor oil. It ran out from the underside, obviously.

I then wiped it down, re-installed on the wheel, and mounted the wheel. Allowing the bike to stand for a day, and catching the remaining run-off in a cloth, I then wiped it down one more time, lubricated the chain as normal, and rode. The sound disappeared and hasn't come back in ~700 miles.

This may or may not help.

Phil G.