Be aware that on one side the large nut has left hand threads. I can't recall off the top of my head with any certainty, but check the protruding threads carefully before spending a lot of effort tightening the nut further.

New drums won't affect the rust issue - the inside swept area has no rust protection new or old. Parking them wet (i.e. after splashing through a puddle) is what rusts them. Or sometimes just the humidity in the air can rust them as well - given enough time. Disc brakes can rust substantially from rain splatter bouncing up of the ground.