From a balance perspective, the altars could be a problem. I'd be concerned that the good guy team would stall a monster they know how to deal with and then position themselves around multiple altars and chain kill several monsters in a row.
I was going to suggest going the Amnesia route and making the it very difficult for the humans to fight back, but you seem to have gotten that.
There are two (free irrc) games I think you might want to imitate: The Hidden, and Morbus (or Gmod Trouble in Terrorist Town, which is similar but wackier and less horror based). In the Hidden, 1-8 soldiers are hunted by an escaped lab experiment called the Hidden, who is near-invisible, has a knife and a few grenades, can leap around and cling to walls, and can attack bodies to regain health. The thing worth imitating about the Hidden is that it let's the player do horror movie shit that has very little gameplay effects. You can steal bodies and then throw them from the ceiling for jump scares, taunt the soldiers in a creepy voice, hide amongst them and attack without warning, or leap around near them to scare them. With the console you can bind a key the lets you become visible, purely for jump scares. Often trigger-happy or terrified soldiers will fire randomly into the air or spin around shooting and hit their friends.
Morbus spawns everyone into the game with a randomly generated name and gives them a 60 second grace period to pick up weapons and find a safe place. Most players are humans, but a few are "brood aliens" that appear human but deal less damage with guns, and can throw off their human skin to become melee-only aliens that turn everyone they kill into brood aliens. They can also re-assume their disguise. The game also sends the humans off on missions, which usually means go here and sleep/eat/take a shower, or you die in a set amount of time. This forces people to split up, and leaves them completely vulnerable for 8 seconds. The result is that humans move around the in small clusters that sort of trust each other, as well as lone wolves, while the aliens try to pick the group apart.
Both Morbus and TTT feature players who are all superficially on the same "team", yet some of them are trying to kill the rest. This creates serious paranoia, and I think could be the concept for a monster. While its true that people can voice chat each other about what's going on, unless some asshole keeps talking after they're dead (which most people don't, and most servers don't allow) everyone is trying to convince everyone else that they're innocent, so no one really trusts anyone else.
One thing to emphasize about both games is speed. The monsters and humans can both die in 1-3 hits (or about a million from a full-auto assault rifle) which adds tension to the game.