I don't understand how the dying status is as harsh as you say. A dying creature could use their action to drink a potion or use a medicine kit on themselves. If anything, not going unconscious right away makes the condition less harsh than standard rules. And yes, a dying creature could still attack, although that would kind of be a sacrificial move, and they can still run away if their exhaustion level allows for it, after using half their movement to get up from prone.To me it honestly depends on what type of adventure you want to play. The dying status seems very harsh, like it may as well be doomed! However the fact that you can still make attacks, and therefore run away (I presume) seems kind of weird to me. You are in a situation where you are on the brink of death every six seconds, yet you still have the strength to make an attack? I like your thinking and see how you are trying to improve combat but I also feel like this is downright abusive to healing classes and marshal classes.
healers loose one of their best tactics, saving the weak, and altogether remove the tactic of retreating when weak to be healed.
Marshal classes are also heavily harmed by this, as you are effectively making the effects of taking damage more severe for everyone, however it is a fighters job to take those hits instead of, say, a wizard in the party.
I like the idea but it kinda seems like it would be best to just run spellcasters with this rule in place.
I don't think it will feel weird when playing. You get bloodied, so you've been hurt and is not fighting at 100%, you then get knocked down but not killed outright and start bleeding. You're councious for now, but could quickly go out if hurt again or if you don't do something about your wound (be it magical healing, a character ability or use of a medical kit). Even if you can't stop the bleeding before going uncouncious there's still a chance one of your allies could save you. To me it feels a lot more natural and fun than fighting at 100% at 1 HP than being completely at the mercy of the dice when you're dropped to 0.
I defnetly don't intend to remove the tactic of retreating when weak to be healed. In fact, the way HP works right now keeps players fighting while low on HP waiting for a Healing Word to save them from death over and over again. From the healers perspective I don't think was taken away, and basically only play as cleric when I play, because this strategy always felt like abusing a bug in the system and trivialized most other forms of healing.
Martial character effectiveness seems to be big concern I didn't antecipate. I'll run the numbers to figure out how much of a nerf this is for them and will try to give them alternatives to make up for it. I think they should have more ways of having/granting resistance or making enemies miss rather than just being a damage sponge. Any suggestions of how to do it?