Did you ever get this problem resolved?
Not yet.
The brakes are loose if there's no drum on them, so the problem is the drum or the pads. I still can't figure out why it only happens when the lug nuts are tightened. The drum will easily rotate before the lug nuts are tight. I can see this being an issue if the drum was too deep and being pulled onto the backer plate, but there is no evidence the backer plate is being contacted. And there's no way the pads are hitting the front surface of the drum, either.
On one wheel I managed to loosen off the brakes (both top and bottom adjusters) and the wheel spins over part of its travel and binds on another part. Makes me thing the drum is not quite true... I've only tried loosening the adjustment on two wheels. On the other it didn't help at all.
I'll be pulling the drums off in the next day or two so I can move the chassis more easily. And I'll retrieve my old drums from the cabin on the weekend to see what happens with them.
-Paul