The first statement: That you want battle to be more meaningful ... and the second: You want PCs to view combat as a risk ... seem fairly unrelated to me.
Meaningful means having a serious, important, or useful quality or purpose. Having a chance for a random roll to kill you has grave impact, but I'm not seeing it providing meaning for the combat. It just adds increased risk that players will lose access to the PC they've built over time. I've had this happen over the decades - a PC with an engaging story walks into a room, rolls poorly to spot the ambush, and then dies due to a critical hit with instant death ... or fails a disintegrate save in AD&D ... or otherwise saw a good story end pointlessly. It absolutely did not add meaning to the combat, or the campaign. It felt like an unrecoverable video game crash that corrupts the save game.
If you want meaning for the combats, I suggest looking at alternate goals to be present in the combat other than survival. Survival as the reason for a combat to exist gets old over time, regardless of the chances of death. To give the combats more meaning, it is more effective to provide other incentives to be in combat and other objectioves to achieve in that combat:
- Fight past the enemies before they can engage something. An enemy cult leader is in the middle of a ritual and you have to fight to where they are (or sneak there) and disrupt the ritual.
- Save someone from the enemies. An NPC ally has been kidnapped and the PCs have to sneak into a lair and get the prisoner free without the enemy killing their NPC ally.
- Protect someone or something from the assualt. The PCs are speaking to an NPC when enemies attack the NPC.
- Keep the enemies from getting away. Someone robs the PCs and they have to stop him before he gets away with the treasure.
- Solve a puzzle before the waves of enemies overcome you or force you to flee. Can you activate the magical artifact before the enemy forces you to flee?
- Race the foes to a target - Two groups are trying to rob a magically trapped house at the same time.
- Stop a reward from decreasing - The PCs find their way to a treasure pile strewn across the floor, but it the floor is collapsing into lava as the PCs fight the guardian of the treasure.
- PCs can't really win with violence, but have to convince targets in the fight to change their views - meaning the PCs can't kill anyone, but they have to survive longenough to change those views.
All of these ideas are things you'll see in TV, movies, comics, books, and other fiction ... but are not used in most D&D games. Instead, most D&D games focus 95% of their combats on survival and pillaging.
If you want the players to find the combats meaningful and care about the combats - this is the focus I'd choose to develop further, regardless of ho well you think you use it now. Thanks Pete
That being said - if you want fear of death to be there, and that is the driving goal, here is the quick and dirty way:
1.) Track hp loss below zero. If you're at 1 and get hit for 7, you're at -6. Apply your negative hp as a penalty to death saves. Yes, this means that most PCs will die in 2 or 3 rounds.
2.) Healing damage at -hp is 2 for 1. If you toss a healing word at a PC at -8 and heal them for 8, they only recover half of that hp total and get to -4 - still dying.
3.) A failed death save deals 5 damage.
Yes, you still die when you hit negative hp equal to your maximum hp. If you want a bit less lethality than all of this, PCs get to use their constitution saving throw bonus for death saves.
If you want to toss in a wound system (where PCs get injuries that hamper you until healed) there are a lot available. i don't use them, but I find that having a deck of injury cards and giving them out if you are hit by a critical hit on the first attack of a turn, or if you go to zero hp, works well enough. The version I built for a friend are homebrew and feature 4 zones on the card with one or more damage types tied to each zone. If the wound is one of the specified types, use the related wound impact. If the type is not present, the PC is not wounded. Each card has a theme based around where the wound is located (digit, arm/tentacle/pincher, leg, lower body, upper body, neck, head, internal injury). If you do not have the body part listed, the DM adapts to make it make sense or discards the wound at their discretion.