Morrus, have you checked out ZWEIHANDER Grim & Perilous RPG yet? It ticks off all of the major themes of a grim, gritty game. It even has a 35 page morally grey adventure in the core book, if you want something that can be ran quickly without a lot of preparation required.
Message me and I will get you sorted for a comp copy.
GURPS definitely does "gritty," if that's what you're looking for, but it will require lots of up-front GM load.
If you don't want to have to delve through all of the bits and pieces of GURPS' disparate sub-systems, and are okay with its baseline magic assumptions, I'd go with Runequest.
Savage Worlds can definitely be "dialed down" to be gritty. By default, I don't find it to be particularly "gritty," per se, but it's simple enough to make it that way.
Lower the "damage over toughness" threshold to cause a wound from 4 to 3 (or even 2)
Disallow "soak" rolls entirely, or require standard soak rolls to succeed at a -2 penalty
Limit the benny economy, either in frequency given out, or limit how many can be spent on soak rolls -- "I'm giving out an extra benny per session, but you can only make two soak rolls in any given session."
D&D. If 5e doesn't work, playing 1 or 2e...or even Basic/BECM for that matter would do the trick.
I don't really think "gritty" is a system reliant thing.
Are the characters in legitimate danger they may or truly may not be able to handle? Is magic somewhat restricted and/or rare? Is healing difficult (and/or, again, healing magic very difficult to come by) and/or lengthy?