I imagine that if it is a catastrophe of the magnitude that means I am having to organize body disposal then I will be digging very large holes to put the bodies in well in advance of filling them with something along the lines of a bulldozer or large front end loader.
I may just dig a very large pit or trench and push trees and other flammable debris into it then dump bodies scooped with a front end loader into it and burn them and repeat as necessary until the pit is full.
My goal would be to first clean up the remains out in the open where they are easily accessible first and then deal with the ones inside buildings after they have frozen or finished decomposing. This may mean burning or demolition of some buildings. Either way the remains end up in the ground whether they are burned or not.
After a mass grave is filled I would place some sort of markers around it or over it to let people in the future know just what kind of ick they may be digging up should they feel the need. perhaps a count of how many people and where they were found could be made and placed on a marker stone.