i'd lay a big ground sheet out on the floor...
get a shovel / floor scraper... get it behind the plaster but over the laths and running in the direction of the laths remove the plaster... leave the laths up though because theyll hold up all the soot and crap that years of victorian living left up there... not to mention any insulation...
then cross battening is a good idea but you can just screw though into the existing joists, depends on how sound they are...
one thing overboarding, but another when its an l+p ceiling and its dead loose... lots of weight in the old plaster but not so much in the laths..