Patching and Plastering - Plaster ceiling repair

A missing window flashing on a window above caused some 80-year-old plaster to sag in our dining room. The leak has stopped, but it did its damage. The wood lath behind the plaster is soft in the center of the area, but of course, I have a huge, jagged section of loose plaster at the perimeter.

I've worked with plaster a little before and not been entirely pleased with the results. This job is very high profile, and I don't want to make our dining room look worse than before. The hardest problem I have always had with plaster repairs is cutting a straight, square hole in it with a keyhole saw. No matter how hard I try, I can't cut a clean hole through the stuff. The wood laths always vibrate with my saw strokes and crack the plaster further out. Not to mention the number of keyhole saws you go through doing that.

I'm considering using a sawzall, but I'm not certain that even that will work. If I saw through all the layers of plaster and the lathing in a square outside the damaged area, would it help to deeply score a line or lay down masking tape, or is there another way to help improve my chances on making a nice, square patch? If it is a good idea, any particular type of blade the best?

Thanks,
Rip

Scoring will help contain any surface cracks. Sounds like the lath is too far gone to strip the loose plaster and let it dry out? Sawzall will work-general purpose blade should be fine although you will still get the vibration it is alot easier on the arm. Why the square- to get to the joists to attach new lath? In some situations where the plaster is sagging but still solid you can screw it back to joists with drywall screws, patch the holes and save alot of area to patch.