Do-able yes. Reliable, so-so.
You are trying to get two thing out of the burn through of the sustainer propellant (there is no thin clay cap nor ejection charge in 0 delay booster black powder motor.) First and most important is igniting the upper stage. You want a quick separation once upper stage ignites, otherwise the upper motor plume will roast the forward end of the sustainer.
The second is deployment of your rear eject system. Before separation, there will be a TRANSIENT pressure buildup in the “chamber “ between the stages, first from the burn through of propellant from sustainer motor and then (if THAT pressure hasn’t already resulted in separation of stages) from the propellant of the newly lit sustainer. As soon as the stages separate, that pressure is vented out the forward end of sustainer.
If your rear ejection “piston” mechanism is really “loose” it will successfully get forced out the back. Emphasize REALLY loose.
In my experience with rear ejection mainly with boost gliders, the really “tight” part is the recovery system. Trying to pack a chute or streamer between the outer body tube and the motor mount I found really challenging, and resulted in considerable friction that sometimes prevented deployment (and remember that is with a “closed “ forward system with a bulkhead or nose cone upfront and using a standard non-0 engine with a cap and delay charge which I think produces more force than just a sustainer engine burn through). Your system by definition has a much shorter duration of pressurization (terminates abruptly with stage separation) and has what I think is a lower initial force of propellant burn through compared with ejection charge igniting and “blowing” through a clay cap. While sustainer will definitely generate a whole lot more force, sustainer ignition should be followed by almost immediate separation, so if normal will be quite transient and IF ABNORMALLY prolonged will barbecue the booster.
That said, try it and see how it works for you. Maybe add some sort of rubber band or elastic pusher system with burn through activation that actively shoves the central core out the back at separation?
Best of luck!
Tom