Add fiberglass rolls across joists in attic if joist cavities not completely filled

Can I screw the blocking instead of nailing it as I'm a little worried the nailing might cause cracking in the plaster ceiling (with wood lath) below?

Absolutely.

Is it okay to sister a 2x6 board to the current 2x6 board along the front and back perimeter of the finished area to support the ends of the new subfloor since I'll be cutting the current subfloor back to the edge of the current 2x6's? Can I use screws instead of nails?

Again, absolutely. Definitely makes things easier.

Should I replace the loose fill insulation with unfaced batts and fill in any small areas with the old loose fill?

Not necessary if over conditioned space, but would not be a problem.

Does all of this sound kosher / is there anything else I should be considering?

The joist are braced by the lath and plaster below on the bottom , and the subfloor on the top so no bridging will be needed.

Remember, heat rises. In the summer the second floor will be hotter than the first for several reasons. I found that after reaching a reasonable amount of insulation in the attic which helps more in the winter season, removing the heat from the attic is the best remedy. I installed a power vent running off a thermostat. You need to make sure you have enough vents around the eve of the house and that they are not blocked for this to work effectively. The cooler outside air will replace the hot attic air and as hot air rises, this happens quickly. It worked for me when I lived in New York, but now that I am in Florida it is even more important to get the heat out of the attic. Most Florida homes have wind turbine vents and several of them to make this effect work. Newer homes here have high ceilings eliminating attics.