It sounds to me like there is a tactics issue more than a composition problem. This is how my guild does that part of the fight.
Form up a triangle with the LK, the Shambling tank, and the ranged/healers. Anywhere in the room is fine as long as they're not miles and miles apart and the Shamblings are faced away from the raid. Somewhere towards the edge (for the ranged/healers) makes life easier for transitioning to the second part of the fight.
Your Shambling tank should grab the first four ghouls that spawn, then the first Shambling, and go back to his spot. You pick up all subsequent ghouls, he'll grab the second Shambling. When the Shamblings enrage, your tank on them should try stun them. If the hunter can dispell the enrage, all the better.
Every Plagued person should run to the Shamblings (the back of them, they have a frontal AoE) and get cleansed within the 5 second window. This sounds easy but people can be a bit ... unaware ... of the debuff at first. Make sure that's sorted. If they aren't near the Shamblings by the time it'll tick, letting them die is always good learning
All DPS should ignore Ghouls and Shamblings and focus on the LK. You can push him right over the 70% mark without worrying about timing.
The raid runs to the edge, the Shambling tank stays in Relentless Winter (avoiding those nasty Ice things and always facing the Shamblings away from the raid) and lets the Plague kill the Shamblings. You'll pick up the first (and possibly the second) Raging Spirit. He'll get the second/third ones when he's back.
Hope that helps

Good luck

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