I have a Skil reversible electric drill that secures the Jacobs chuck in this manner. There is a left-hand-threaded flat head screw that goes into the end of the spindle inside the chuck, that secures the chuck from unscrewing when the drill is operated in reverse.
Admittedly, this is in a solid spindle, but the idea works.
How about a left hand threaded bolt or tube through the spindle bore
that clamps the chuck or backing plate to the other end of the spindle
with a left hand threaded nut? ...or some more clever kind of lock,
maybe a cam-over sort of thing?
That is just the first thing that came to mind...