Yeah moving computers around is not one of fog strong points. My guess is your will need to do some coding on fog, to get it working.
I know there is talk about how to address the moving PC around issue on the developers forum here
You could probably make a script or something, you could run in the PXE boot menu, that will just look at the ip address that computer got, send it to fog and have fog automatically remove it from the last group and add it to the new group that is assigned to the IP range. Then send a re image task using the image assigned to the new group to the computer.
I am just talking out loud here, I really don’t know much about how the programing works in fog, I am more of a network guy.