Can't you just pass the encrypted message further without decrypting it? Of course, there needs to be the same decryption mechanism on both sides, but it doesn't make it impossible.
Then there's the issue of syncing those messages between Element One clients which means the client now has to re-encrypt the messages and send them back to the server. And if the client is responsible for fetching messages then providing push notifications will be very difficult.
So if you can actually decouple polling/listening for messages from decryption then it would probably be possible.
A brute force approach would be to provide an open source, self-hostable server but can be configured from the centralized Element One service. This server would hold the actual service tokens & decryption keys and would just be sending re-encrypted messages back to Element/Matrix.
The server/bridge is not opensource? I see their github account has lots of code.