Posting what I've found on this so that others who are curious may have something to go on...

The closest I've found on this "inbox relay" is an inference based on NIP 65 suggestions `DMs SHOULD only be broadcasted to the author's WRITE relays and to the receiver's READ relays to keep maximum privacy.`

https://github.com/nostr-protocol/nips/blob/master/65.md#final-considerations

So for each user you want to send a message to, before doing so, may need to first request all 10002 for that target pubkey from whatever relays you normally read from, and then parse for those that are not marked strictly for "read" purposes? Or maybe the suggestion is written backwards since they will be reading from that relay. Probably best to just try to push the DM to all the relays the user has announced in their 10002 event, and ignore any relay error messages as temporal.