I take a system inspired by the video game Wildermyth, where the player gets to decide what happens at 0 HP.

Option 1: You fall unconscious. Your fate is out of your hands.
Option 2: You die, but… You might go out in a blaze of glory, or inspire an ally, but you’re dead for good. At least it’s a good death, which is better than some get.
Option 3: You live, but… You might lose an eye, or a magic item gets destroyed, but you manage to escape. You’re still out of the fight, but you live to see another.

I have recently encountered ICON and come to really like its dying mechanic. Each time a character is reduced to 0HP they become incapacitated, but stable, and gain a wound. Each wound reduces max hp by 25% and only goes away after an adventure (quest). A character can help an incapacitated character (rescuing) bringing them up and healing them to their new max HP, which after one wound would be 75% of max. Second time dropping to 0hp, a second would and new max hp of 50% of original.

It gives good longevity in individual encounters and forces caution in the longer run.

Dying: at the end of your turn make a flat check against DC 10. If you succeed remove one from your Dying Condition. If you succeed by 10 (eg. you roll a natural 20) remove two from your Dying Condition. If you fail to succeed add one to your Dying Condition, if you fail by 10 (eg roll a natural 1) you add two to your Dying Condition. You are no longer incapped when you are at Dying 0, add one to your Wounded condition. If you have reached Dying 4 you are dead and can only be resurrected through magic. When next time you get the Dying Condition, you dont start at Dying 1, instead you start at Dying 1 plus your Wounded Condition Value.

If it takes a half hour for a single round of combat then I will assert that you actually are doing D&D wrong. Players should know the rules for anything their character can do and be paying attention so they’re ready when their turn comes up. Combat and magic rules take up maybe a dozen pages in the PHB, spend an hour and read over them a few times to make those weekly games you invest two to six hours into go much smoother.

The DM should know all the rules. Like most homebrew I see, this is an overly complex “solution” that functions nothing like anything else in the game and wouldn’t be necessary if everyone involved actually learned the real rules. 5e already has an exhaustion mechanic and it works nothing like what is described. Making up new and convoluted rules to be used by people that take six minutes to move and make an attack or cast a spell is not going to accomplish anything but making your combat turns forty minutes long instead of thirty. I play in a game that includes seven PCs including two “lightly experienced” players and one complete noob. Combat rounds take maybe ten minutes, tops, because people pay attention and the DM actually learned all the real rules.