Can I repair an interior door if it is fractured around the knob?

The handles on several of my doors were pulled on too hard by my children. More than likely they were hanging from them at one point.. I have seen quite a few videos that show repairs on holes that are on in the middle of the door somewhere. They generally show filling the hole most of the way with foam and then finishing with foam, filling with plaster or bondo (weird), and then finishing with spackle.

Is there any way this is going to work out well near the handle? Will I be able to cut the hole to size again, or will the plaster/foam fix just crumple during cutting or after the knob is reinstalled?

I'm not looking forward to replacing the doors and then cutting an inch off of them to install. For some reason mine seem to be 30x79"