After some investigation and benchmarking, it looks like the best PIR protocol for this use case is YPIR+SP (from February). On a single compute- and network-constrained server, with users on constrained (and possibly metered) networks, this would amount to providing service to up to 1000 users while keeping latencies reasonable; by (quadratically) scaling the server(s) enough, that could become up to 100,000. That means this method of message routing could definitely work, although I look every day in case new protocols are published.
Thanks, it’s late here now but I’ll try to look soon. I didn’t realize significant improvements over Goldberg etc al were really possible. I’ll try to understand that too.