Home user can't see headless Plexamp in player list

Not sure what you mean by this.

The Pi has an IP address.
The Android and iPad have IP addresses.

For the owner/main user, it can use plex.tv hints to find the players; shared users rely on network discovery.

If you post the Plexamp logs from the owner’s Plexamp which does see the player, we can see what IP address it’s trying.