Twitch always creates new products, like this, quite restrictive but does loosen them up when they see a valid use.
For now, you can submit your request to uservoice, or vote on one that fits your needs:
Twitch keeps looking at and evaluating them.
A compromise I could imaging would be to keep editing the rewards locked to their “owning” client ID, but all clients being able to process the redemptions, for example.
Or some kind of “permitting” another client to affect other rewards.
Let’s see where this goes, the API still quite new, a lot might change 