How about we remove avatar tokens altogether and make them a one time buff given by the altar.
Once buffed, you’re given a temporary special ability to summon said avatar. During which time a new GUI element will appear onscreen associated with a keybind to summon your gods avatar.
Additonally to prevent the duping of items to generate zeal we also remove the ability to collect and store said items in your inventory. So no one can interact with them and perform a dupe.
For example, lets say you go to collect hearts for Set. Upon harvesting a body, you generate a heart point visible onscreen as a GUI Element instead of an item. Said point cannot be traded, dropped, interacted with, and does not exist in your inventory. Upon death they are lost to the world and deleted. Upon interaction with a Set Altar they are inserted much like thralls are to a Wheel of Pain. You can still use them to craft once inserted into the altar but you cannot interact with them beyond that.
Additionally and though not a solution but more of an aside, as I feel players should be more noticeable when essentially carrying a weapon of mass destruction; if and when a user is empowered by a God, said individual would emit a bright aura and light associated with their god visible even at night.