I would have suggested to look at the rims to make sure you don't see any cracks at the spoke holes but usually for me those only click as slow speeds and while climbing. You are sure the crank is free and clear from anything, correct? I mention clearances only because I had the plastic over the guard on the chain stay near the bottom bracket to fray outward before and it was hitting the crank.
Have you tried different wheels or skewers by chance to see if that makes a difference? My brother had a noise that was somehow related to the front wheel and skewer moving ever so slightly.
__________________
Ride your Ride!!