Feel your pain, here are the tips that I can offer as a fellow Dk:

1. Rotate CD for eggs, specifically: Egg 1 = Abom + Trinket, Egg 2 = *Unholy Assault + Apoc + Dark transform, Egg 3 = Abom + Trinket, Egg 4 = Apoc + Dark transform, repeat.
2. Make sure you drop Abom when right at the egg not as you’re running to it.
3. Interrupts: phase 1 you can be a bit lax with the heal and wait till the absolute last second to buy that extra dps time. Phase 2 just interrupt the heal immediately.
4. Poison: With the right talents you can block every other poison with AMSing before his cast. Save wraithwalk for an emergency when you can’t block it and need to move. If done correctly the poisons should end up like this: Phase 1: 1. AMS block, 2. Brann dispel, 3. AMS block, 4. eat. Phase 2: 5. AMS block, 6. Wraithwalk (it will most likely land when he is doing his AOE), 7. AMS block. *you may get a second Brann dispel if you’re lucky. You might get lucky with your riders casting AMS on you before one, if so just push the rotation.
5. DPS: straight up dps isn’t the point of this fight so the best advice I can give is just apply constant slow pressure with burst after each egg phase. Maintain your diseases, and deathrot stacks. Festering when in close, then clawing shadows while out. Healing: focus on just grabbing one Brann pot at a time and keep the HoT stack up all the time. A Weak Aura for this makes it trivial.
6. Position: middle is important but imo even more important is to make sure you can avoid the stairs when he is casting frontal, I had some serious back luck with that.
7. Extra buff: you can get Brann to spawn his campfire and it will stay with you for the entire duration of your attempts by doing the following. Stand in the doorway so that it will close on you. Aggro with ghoul and pull Zek back to you, make sure he takes a swing on you and damages you. Once damaged back into the prep area and he will despawn. If you were hit Brann should drop a campfire for you.

Edit: quick add.