How to remove blown in attic insulation

I would clean out the area around the holes to give myself room to work without being showered with cellulose. Open the holes a little: make them square, and big enough to be able to get your hands through. Next, get myself a roll of R-13 fiberglass batting (currently less than $10 at Lowe's or HD), and cut patches to fill the void in the cellulose insulation: you'd probably need two or three layers, depending on what size your ceiling joists are. Stuff them through the holes and spread them out. Finally, use a couple of 1x2's to cross each of the holes, and patch them as described in this answer to this question.

I've used a shop-vac for cleaning up blown cellulose, but for disposal, not for later re-installation. It seems to me that it has a very different texture before and after: clumpy and with some structure, versus powdery, no texture.

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.