> What happens when you move the fuel?

It stops reacting. If you blow up a nuclear reactor you've made a nice radiological hazard (though Uranium/Thorium themselves aren't particularly hazardous), but as soon as the fuel stops being contained inside of the appropriate neutron-mediating environment and is scattered, it will become subcritical.

The question of whether or not deploying nuclear reactors in warzones is a good idea is entirely different from the question of whether meltdowns are a realistic possibility. A critical nuclear reaction can be sustained with neutron reflectors and moderators using an amount of fuel that would otherwise be subcritical. Any "reconfiguration" only reduces the criticality factor of such a reactor.

Even if a meltdown doesn't happen, if such a generator is struck by, for example, an artillery shell, who is going to clean up the mess?

Then the reaction stops because it's no longer in the presence of a moderator.