I have a 115-year old building that had plaster and lathe over rough cut 2x12 ceiling joists. After removing the plaster and lathe, I have found that the joists are upwards of 1/2" off level from one joist to the next. Additionally, there is bridging between the joists that extends to the bottom of each joist. How should I level this without destroying the stability of the bridging?

Normally these old places were prepared for ceilings by adding strapping ( also called furring strips) 1x3 or 1x4 to the bottom of the joists, perpendicular @ 16" oc. Use shims to bring them to a string line set level. Nail up with ring shank nails.