The squeak only happens when the freewheel is receiving pressure. I can turn the crank to a level just before this and no sound is made.

How much side to side movement should a rim have in relation to say the center line of the BB? This sure seems loose at about 3/16"+ each way.

The sound is similar to taking lapped spokes and squeezing them across each other.

The hub has no visible slop.