Insulation of an unheated workshop

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.

Dense-packed (and only dense-packed, not loose-blown) cellulose is better in walls than fiberglass batts, for a couple of reasons.

1. It has a slightly higher R-value per inch.
2. Is is hygroscopic, meaning that it can take up moisture; in doing this, it can protect the structural wood should it ever get wet.
3. Dense-packed cellulose can improve the airtightness of a stud wall; Fiberglass cannot, and is very strongly negatively affected by a non-airtight wall (furnace filters are made of fiberglass, which shows you how much air can move through them!).
4. Cellulose is loaded with borate, which makes it pretty much mold-proof. Fiberglass can, paradoxically enough, grow mold if it gets wet and stays wet, especially with the kraft paper facer.

That said, unless your fiberglass batts are wet or moldy, it's probably not cost-effective to remove them, especially if leaving them in means you can avoid tearing off perfectly good drywall. The kraft paper facer on most batts is not a vapor barrier, it's a vapor retarder, which is fine. Very few batts have foil facers, which are vapor barriers. Even if your batts have vapor barrier facers, I see that you live in Wisconsin, which is a place where you can get away with having a vapor barrier without it being too bad (most of the time you don't want a vapor barrier in your walls). I'd leave the batts in.