No Stamina Challenge
I got this idea from Challenger Andy and I did it (with deaths) some time ago, but I only just now finished it deathless (nightmare difficulty). And I really cannot recommend it enough. I think it's absolutely perfect for a second, more serious and scary playthrough.
What does it mean? You're not allowed to use stamina in any way. That sounds more complicated than it really is: You're not allowed to dodge or sprint, and you're not allowed to use melee weapons. The only other thing you're not allowed to do is throw a knife, which is somewhat unintuitive because that is the only thrown weapon that uses stamina.
What's great about it is that isn't insanely brutal. It would be quite harsh on a first playthrough, but you absolutely don't need to have the entire game memorized to succeed. I walked into what turned out to be a trap where you're attacked by 4 or 5 red chompers in my playthrough. Being precautious enough to always wear armor and carry my assault rifle everywhere I went, and having the presence of mind to switch to it as soon as things started to go south, was enough to barely survive.
But you do have to take threats seriously. You can't just run away from enemies. They're all faster than you. If you do flee, you'll have to constantly dodge attacks or hide behind obstacles. And when you do choose to fight, it's a genuine drain on resources. In the early game, using a molotov cocktail or a pistol magazine really drains your bank account. Not so much in the late game, but at that point, a day full of serious fights will cost you a lot more than that.
I didn't do it, but, honestly, you could ban or restrict skills as well. I would lean towards just restricting, because a lot of them are interesting, and it sucks to turn mushrooms into a completely worthless resource. But Scream and Chameleon are REALLY broken. If you don't panic and remember to use them before it's too late, they will easily get you out of every sticky situation that you can find yourself in.