I have recently completed cursed modes ee on tier 3, and I have now unlocked all rewards seen within the menu.
Currently you are able to achieve 8/9 relics as the final 1 is still unfound. Unfortunately you'll have to complete this boss a minimum of 4 times, once for each tier and an additonal time for the Dragon Head relic.
This is due to the game not retroactively unlocking the previous tier of rewards for completion of higher tiers.
You are able to unlock the base ee rewards within cursed mode, as well as interacting with the tablet post ee. You're just unable to activate relics until you do so. However you are able to join someone who has these relics and earn the rewards that way if you don't want to earn them youself. (Looking at you Bus and Dragon Head)
For tier 3 I'd reccomend the following relics; Dragon Wings, Teddy Bear, Vril Sphere, Focusing Stone and the Dragon Head. As you're able to bypass most of these effects.
Power-ups spawned via gobblegum bypasses the Dragon Wings relic.
Perkaholic can bypass the Vril Sphere in addition to the free perk at exfill 115, however this one makes it so that perk acquired is repurchaseable without taking 1 of the 4 perk slots, and cannot be changed, so be careful of your choice.
Focusing Stone disables self revive kits, I'm unsure if it's a bug but they can still be acquired by completing T.E.D.D trials randomly.
I reccomend using the Dragon Head over the Bus or Blood Vials, as the health regen is fast with the Bus and does affect the ee boss fight. And augments are super useful, as vulture aid can be used to bypass ammo boxes.
The calling card for tier 3 cursed isn't animated for those going for it, however the alternate pap camos are clean and for me are the better rewards.
I am curious to see if there's any additional rewards for all 9 active and beating the ee or for future zombies maps.
[Completion of each relic trial for the first time will give a gobblegum, I believe this to be set so the Dragon Head will always grant you a perkaholic]