If you guys were going to House Rule a DEADLY D&D5E set of rules what would they be?
I value parsimony, so I'd try to keep the rule changes small. I would do three things, assuming that we're doing a dungeon-crawl style game centered on combat:
(1) Make most encounters in the dungeon somewhere between quadruple-Deadly and 10x Deadly. This makes a straightforward brawling strategy barely possible but very difficult, and rewards Combat As War thinking.
(2) Whenever you are incapacitated/stunned/paralyzed/unconscious (but not grappled/restrained), your Dex modifier is -5 instead of whatever it usually is. Won't affect PCs in heavy armor, but that swashbuckling rogue is in deep trouble if he ever gets paralyzed by a monster or put to sleep, even briefly.
(3) You can go below zero HP. Instead of the normal rules on death saves and stabilization, you die whenever you reach negative (max HP). E.g. if you have 40 max HP normally, you die at -40 HP. When you are at zero HP or below, you are either stunned or unconscious. (If you choose to make a DC 15 Con save and succeed you can be stunned, but if you fail the save or choose not to try, you are unconscious from shock.) When you are below zero HP and have not already stable, you must make a death save at the start of every round. If you succeed, you are stable unless/until you take damage again. If you fail, you take 20% of your max HP in damage, rounded UP, not down. You can be stabilized by another character's actions as usual, through the use of a healer's kit or the Wisdom (Medicine) skill.
Example: if you have 40 HP normally, and you get hit twice by an Iron Golem for a total of 50 HP of damage, you're now at -10 HP (and likely unconscious, unless you made the DC 15 Con save). Since you're at -10 HP, not zero HP, you can't be restored to full activity by a simple 1 HP Word of Healing as you would under PHB rules--it takes 11 HP of healing to get you conscious again. At the start of every round, you make a death save (as usual, it is DC 10 and no attribute modifiers apply). If you succeed you stabilize at your current HP, otherwise you lose another 8 HP and must save again next round. If you ever reach -40 HP you die.
Remark: In some ways losing 20% of your HP is more generous than the default rules because it only takes one roll to stabilize, and someone who is just barely at negative HP may take five failures before they die. A wound which takes you down to -1 HP is extremely unlikely to kill you. In other ways though, it is less generous because stabilizing doesn't wipe out past failures--that requires actual healing. Furthermore, if you're deep in the negatives, a single failure will kill you, possibly before anyone else can intervene.