It may not be possible to fit the safety dogs , as I call them, to every lathe.
On my lathe, Engineerrs Tool Room BL12/24 (similar to Chester Craftsman, /WArco BH600 / BH900 ) the chuck backplate has a short parallel portion which butts up against the flange on the Mandrel. This parallel portion has two, diametrically opposed, tapped holes, each of which is used to secure an angle "bracket" , one end of which locates behind the flange on the mandrel. In this way, if the chuck tries to unscrew when running in reverse, the dogs prevent the chuck uncsrewing far enough to come off.
If I knew how to post, I'd take a picture and post it on here!
If this can be applied to the OP's lathe it will only prevent the chuck from unscrewing.
The problem here is that, currently, it WON'T!
If you have a mandrel handle, you could try putting a wood block, as shown in the picture at the start of this thread, under a chuck jaw, and using the mandrel handle, turn the mandrel briskly backwards, so as to hit the jaw hard against the block . After all, this is the process that hammered the chuck up tight, so a little low speed hammering in reverse may loosen it. I would not suggest doing this under power, unless you have a VFD with a JOG facility, which still leaves you able to remove power immediately.
Howard