There’s no conflict - you have 660 Burn and only one Fire / Elemental conversion so it’s converted to Physical.
Also “No matter where the Conversion occurs though, it is only applied once.” so it’s stays Trauma.
what happens is, any base phys you have, like the entire Forcewave line, becomes fire dmg from the necklace
any fire base, like the burn on necklace, becomes phys
resulting in weird mix 2 dmg types, - also worth to note the fire->phys on necklace takes priority over shard of beronath conversion, (since amulet is transmuter level and beronath is global), so any base phys dmg, 12 flat on a ring or devotion etc will always become fire to forcewave