What level would you set such a game at? What would you use as a premise? Would you nerf clerics by making the zombies "infected" or let clerics shine however briefly before they run out of juice? Would you make it an escape, a dungeon crawl, a quest or something else?
Good question. I've been running
Tomb of Annihilation, and there have been plenty of zombie encounters. What I realized very quickly is that the real excitement in facing zombies is not in the mechanics of the combat, but in the overall scenario in which they're encountered. In other words, I started thinking of zombies as
hazards/puzzles to be overcome, more than just monsters to defeat.
Here are a couple examples from my game...
Yellow Musk Zombies & Cannibals with Pit Traps. Already familiar with zombies, PCs encountered a ruined elven treehouse village with zombies milling around below. These zombies were different, however, with roots growing over them and yellow flowers blossoming from their heads. Zombie-eating cannibals lurked in the treehouse above, and they preferentially ate
yellow musk zombies for their intoxicating effect; thus the cannibals lived in a sort of "truce" with the yellow musk creeper which they treated kinda like Seymour from
Little Shop of Horrors. The cannibals set up pit traps around the area to make zombie harvesting easy. The PCs were nearly overwhelmed, but upon discovering the pit traps were able to turn those against the stupid zombies which shambled right into the pits. Also led to some interesting role-play with the cannibals.
Zombie Mirror of Horror. PCs were at a mirror puzzle-door at a temple at the top of a waterfall. Once the PCs assembled the mirror shards, zombie versions of all creatures reflected in the mirror began pouring forth. Only way to open the puzzle-door was to leap through the mirror which acted as a portal to the Border Ethereal plane, so half group held zombies at bay (I had fun describing zombies appearing like certain PCs/NPCs) while other half slipped through the mirror. The ones on the Ethereal encountered a distance-distorted misty hall full of shambling zombies (with some zombies looking like their ancestors or deceased loved ones), and at the far end of the hall was a black-and-white glowing handprint where the puzzle-door would be on the Material Plane. Getting past the zombies and touching the handprint opened the puzzle-door & stopped the zombie incursion into the Material Plane. It made for a creepy fun little puzzle.
Past Adventurers in a Magic Pit. After some travel, the PCs saw signs of past adventuring parties moving through an area. They were invited to a stork-man (eblis) village. While enjoying a "trade feast" hosted by eccentric eblis, some of the PCs got curious/greedy about the treasure the eblis chieftain kept hinting at. Half the party was escorted to examine the treasure in an ancient dying hollow "tub tub tree" which creaked like groaning zombies in the wind.

The floor was enchanted to dissolve upon a certain command word being spoken, which the eblis chieftain tricked the PCs into saying. They fell 40-feet into a pit full of zombies of past foolish adventurers, with their fingers worn to the bone from trying to crawl out. One PC even fell on a zombie! Half the zombies had their eyes pecked out by eblis – which would make them immune to the eblis' innate
hypnotic pattern spell. It would have been brutal, but thanks to a fast-thinking player casting
darkness at the entrance where the eblis were, they were able to escape with their lives (and some loot).
To answer some of your specific questions...
Reynard said:
What level would you set such a game at? What would you use as a premise? Would you nerf clerics by making the zombies "infected" or let clerics shine however briefly before they run out of juice? Would you make it an escape, a dungeon crawl, a quest or something else?
If it's a one-shot? 3rd-level is usually what I do for one-shots with mostly experienced players.
For premise, I'd suggest something simple for a one-shot (e.g. find/stop the necromancer), and then introduce a single twist (e.g. the necromancer is sympathetic and has simply lost control of his magic).
No, I wouldn't nerf clerics. Let them enjoy Turn Undead. Design a scenario which accounts for this by presenting an opportunity cost (e.g.
another plot-specific use for Channel Divinity) or multiple encounters before having the option to short rest (e.g. a time-sensitive quest).
It can be any of the above, but I'd tightly define the party's quest, and start them right in the action. No meeting in a tavern, buying supplies in town, questioning the quest-giver. Start them right in the action. A tense search through a market breaking out into a chase or a fight is a good bet.