+1 for the "strip" method.
I like using carbide blades on a sawzall... if the lathe is loose, try mounting backing boards on either side of your cut - lengths of 1x3 mounted on the surface of the plaster (with long drywall bits to the joists) to keep it from shaking loose with the saw.
Make sure you have an exhaust filter on the shop vac, or a "near HEPA" filter for the dust!
