Having a ground connection to the 1050s chassis is not going to buy anything except some extra safety in the remote chance that AC potential makes it's way to the chassis.

Balanced power is good for canceling out any common mode crud that is picked up on the power lines. To take best advantage of it though, the hot setup would be to use the balanced 220 VAC feed from the power pole and step it down to 120 VAC in the balanced power transformer, keeping it balanced. Then there would be common mode rejection benefit all the way back to the power pole transformer, and possibly beyond that.