MarkB
Legend
My only word of caution is that by 20th level a great weapon fighter can output an average damage of around 240 for two rounds using action surge. If you limit HPs too much for monsters you'll kill stuff much faster than you might expect.
Actually, that is pretty much in line with my expectations. From the playtests, my impression is that 5e combat only lasts a handful of rounds in any case. Any measure to reduce hitpoints at high levels will almost certainly reduce that figure down to about 1-2 rounds, with monsters going down in a couple of hits and PCs not faring much better. Whether that satisfies the OP's definition of 'gritty' I'm not sure.