Faced with a similar issue many years ago I simply said “stuffitt” and put three tapped holes in the rear part to pull the back off.
Easy enough to measure the depth of the back part and set up so I didn’t drill too deep.
Obviously the main body ended up with three shallow conical holes to accommodate the tip of the drill but, pragmatically speaking, this would clearly make no difference to the performance of the chuck when it was rebuilt.
Clive