Does the inter-floor insulation in the 1911 home contain asbestos

Actually, since you are primarily concerned with heating conditions, the vapour barrier goes on the warm side of insulation, meaning right up against the sub floor boards. This is to keep moisture from the house from condensing in the cooler insulation. Outside moisture would not condense in the insulation as it should always be warmer than the dew point of the outside air, though in the UK it may often be a close call.

Loose fill generally provides a more complete insulation job, filling the whole space completely. Batt insulation is much easier for DIY work. Even if you access from below, loose fill may be possible. You could actually install loose fill by cutting a hole in each joist bay, instead of removing the ceiling. The main problem is you have no way to verify the void was completely filled. It is highly dependent on the skill of the installer. It also negates the ability to place a vapour barrier, but depending on the flooring system, it may not be a serious issue. In your case though, it is probably an issue.

If any recessed lights are in this space, if they are not rated for placement in insulation, they will need to be replaced. If you go in from the ceiling, it will be hard to get a good vapour barrier. Just do the best you can, sealing it well to each joist. You'll have to allow the joists to be part of the barrier. It may be worth spraying them with a quick latex primer coat to help make a better barrier.

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.