Correct me if I'm wrong but this seems to add overhead for no reason versus just sending the event IDs of what you have. Why add the overhead of the tree unless you want proper inclusion proofs (which would require merkelizing all events you have as a relay).
Discussion
The hope was to tmget the tree or a bloom filter to reduce the amount of IDs. Amethyst generally has 50,000 IDs in the local database, which would make it a 3mb upload at every new filter request to a relay.
Merkelizing IDs though is just going to add more data, or if you dont send the whole tree add resource demands for relays to hash the tree from inputs.