Exposed lath and keys on entire ceiling
I would:


rip down all the remaining lath and plaster.
check how level the joists are
fix up any crazy out of levelness with shims/wedges (depending maybe apply new furring strips)
rent a drywall lift - they typically reach 15'
install the drywall boards
hire a drywall guy to do the mud / tape / sanding (unless you already know how or feel like learning that part).