Ancalagon
Dusty Dragon
I would go a very different route, because IMHO the abundance of healing is not the problem.
It's not so much how easy it is to bounce back to full health, but rather how really dangerous it is when your health is low, and it isn't very dangerous. IMO if you slow down healing, all you get is that the PCs will try to withdraw and rest more often. The main result is that you'll get less encounters per day, but lethality won't increase much.
So then you would need to force more encounters, or use bigger monsters, but this you can do already, without the need to house rule HP/HD/healing.
More and bigger monsters certainly helps to push the PCs towards the "danger window", but compared to older edition IMO that window is not as dangerous. The main reasons are (1) death saves, (2) options to stabilize, (3) revivify. In addition, the whole 5e is remarkably (4) lacking save-or-die spells, and even (5) save-or-suck spells often offer repeated saves every round. Finally there are (6) no "death spiral" effects such as level drain and ability score damage.
So if I wanted an overall more lethal 5e, I would consider tinkering with those, maybe change just 1-2 of them at a time and see how it works.
If you re-read my post you will note that I proposed (2) and (3) on top of changing natural healing.