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This is an interesting idea, but I do have a question on op-sec. What is the functionality of the push notifications? I know that Session has a weak point in that LE can corolate the user ID to a specific device by sending a message to that ID and timing the push notification through Google's servers.
Session gets around this by letting you disable Google notifications and rely entirely on their decentralized communication network at the cost of speed and reliability (notifications can might take hours, and even sometimes just not go through).
There are no absolutely secure systems. Any tool that calls itself secure is still a compromise between security and convenience. However, you need to be reasonable and not invent something that LE will never do, since the solution you described is ineffective.
If you are so afraid of Google services, use special operating systems without them.
That is completely understandable. I am absolutely not saying this shouldn't be implemented. A delayed and unreliable system would be an antithesis to what you are doing. The ability to have instant notifications of important forum activity would be a great boon to those doing business here.
I was only asking because it's an issue I've seen discussed before (and couldn't find any suitable answers quickly [they may be burried in the documentation] on the Matrix or SchildiChat pages). I guess it is ultimately a fairly moot point because if the BB private server is compromised we all likely have bigger issues than push notifications.