As a former Mormon, I can see that first idea being absolutely hilarious if implemented correctly. I'm imagining all sorts of increasingly absurd scenarios you could place the Mormon main character in and the kinds of jokes you could make, there's a lot of potential haha. Stuff like coffee and tea being special attacks that the bosses can use, or dialogue with lots of really unusual swear substitutions. I think letting the player die and having the degree of heaven they get into be based off of their score in-game could be a really hilarious feature.

I think mixing in just the right amount of janky ragdoll physics and glitchy NPCs would actually augment the game, and I could see it being a game that streamers and their audiences would find funny too.

There would definitely be some ultra-strict/traditional Mormons who would be offended by a game like this but I'd say the vast majority of the membership would find it quite entertaining.

Edit: Could call it Mormon Missionary Simulator to both give the game a slightly tighter focus/story and also indicate that it's part of the wider genre of "XYZ simulator" games that are often pretty absurd and funny.