Ta Phil I did wonder about using temperature changes but in my case I was thinking of filling the air gap under the Bakelite (I had one out years ago and recollect that the bottom of the Bakelite is recessed hence the air gap) with water and then bunging the assembly in the freezer but had/have visions of shattering Bakelite.
Which prompts the idea injected expanding foam
I have also tried the compressed air thing but half a dozen hands are required and I was on my own and the pressing upwards on the inside upper surface of the battery compartment thing.
Another idea that comes to mind is, and excuse the crude diagram, to drill the heads off the two 'hidden screws' through the base so that the remaining threaded portions are free of the outer metal case.
From memory there are nuts and washers on those screws in between the Bakelite and the metal case.
Then rig up some form of bridge puller that attaches to the remaining screw threads and sits on the upper edge of the metal case.
Tightening the grey "puller nut" would tend to pull the Bakelite case.
Of course it could also pull the 'trapped' nuts though the Bakelite
With regard to Rob Lines' problem, since his principal motivation for removing the case was to gain access to the screws holding the battery compartment in place would drilling the metal case in locations corresponding to the battery compartment screws be an alternative solution?
It would expose the screw heads and allow them to be unscrewed or drilled off and the std battery cover would cover the new holes in the metal case.