It's hard to find a good-balance middle ground IMO. Most house-rules either nerf things into non-use or make the game super-lethal. Like many, I find the 0 HP to 1 HP and suddenly up and fighting a bit too bizarre, but DM's who play hard will tap-tap downed PCs to death.
Could we have a "recovery" mechanic for PCs who reach 0 HP and are down/disabled, that allows them to slowly get back into the fray, hopefully maybe encouraging further healing? Something like:
Round 1 (after being restored from 0 HP): disadvantage on attacks, ability checks, and saves. half speed. (this way you can
ONLY stand with your movement)
Round 2: half speed still, disadvantage on ability checks (you're still shaken)
Round 3: disadvantage on ability checks
Round 4: you're good to go!
Penalties would last until the start of the next turn. Each spell level of healing or level of strength of a potion of healing speeds up the process by 1 round maybe? A successful Wisdom (Medicine) check (DC 15 or 20?) could also remove 1 round of penalties?
Example. Suppose you have 0 HP and another PC casts Healing Word from 20 feet away. You gain 7 HP. But you have all the penalties listed above (disadvantage on attacks, ability checks, and saves. half speed) so the PC moves 20 feet to you and also uses their action to help you drink a potion of greater healing ("level 2" in strength), giving you 16 HP more. The potion also reduces your penalties as if you had already recovered two rounds (so you only have disadvantage on ability checks) on the next turn when you act.