Framing – How to Secure Solid Blocking in Joists Without Staggering

You should shim under the loose joists with steel shims, not cement, because cement causes wood to deteriorate. Large galvanized washers and small steel plates can be used as shims. The framing block in between the joists are called bridging and in an old house I would space them about 4' on center. You can off set each row by 1 1/2" which will enable you to blind nail through the joists which minimizes toe nailing. Use 3/4 tongue. And groove ply glued and screwed to the joists and bridging. I would use pl400 for glue and 2" exterior screws spaced about 8" apart. If a second layer of ply is desired you should also glue and screw it the same as the first sheet. Try to hit the joists. Use a chalk line to mark the joists. If a solid wood finished floor is being installed 1 layer of 3/4 plywood is all you need.if a ceramic tile,stone or wood laminate floor is going in use 1/2 ac plywood over the sub-floor.

Unfortunately, as with most questions like this, you're going to have to talk to an engineer. A bunch of amateur DIYers on the internet, is not the proper resource for this type of information.

You're making a major structural change to a building, and you don't want it to cause property damage or personal injury. The "correct" and responsible thing to do, is to seek the advice of a trained professional.