Burning Wheel would be a good fit, as it starts out fairly gritty. I'm starting up a new BW campaign myself, and one of the setting options I'm pondering is a home-brew world inspired by Lamentations of the Flame Princess: Grindhouse Edition.
I'd use the system as-is, for the most part. About the only thing I'd tweak is magic, and lot of that comes down to what you mean by "low magic." I've seen that term used to mean magic that is ...:
- ... weak but commonplace.
- ... powerful but rare.
- ... powerful but not flashy.
- ... or some other combination of power, how common it is, and how flashy it is.
There are a lot of things you can do to achieve the feel you want. You could probably leave Dwarven magic as-is. It mainly comes down to the Dwarven Arts (crafting items which are better in some way, such as a small mechanical bonus to whatever the item is used for), and Rune Casting, which the dwarf can use to reveal another's dire fate.
Elven magic is in the form of songs, which are subtle but can be powerful. They can hide the singer from sight, add to weapon skill, ask a door what lies beyond, and the like. Personally, I'd have to seriously consider each individual song and whether or not to allow it in a low-magic, dark-fantasy game, based on what those terms mean to me.
Orcish magic, Rituals of Blood and Rituals of Night I would absolutely leave in as-is. Rituals of Blood involve sacrifice and aims to summon allies, transform the caster, or twist enemies. The effects are whatever the caster wants, with example effects ranging from implanting a doubt in someone's mind or summoning a wolf, to summoning every earth-bound demon within a hundred miles or driving an enemy insane. Rituals of Night are orcish sorcery, with a set list of spells. Probably the flashiest is one which causes a haze to partially blot out the sun creating a dim twilight for miles around; very flashy, but perhaps excusably so in a dark-fantasy game.
Human default magic could be a problem. Sorcery can be risky, calling for care and caution on the part of the sorcerer. Failures can wreak havoc across the region in various ways. But the spells can be powerful and flashy, such as White Fire (essentially a lightning-bolt spell); as an aside, this is an example of a spell which is risky even it if succeeds, as there is a chance of it leaping from your target to another individual in the area, with equal chances of hitting friend or foe. If I were to include sorcery, I'd review each spell and decide whether or not it fit.
Alternatively, I'd grab the Magic Burner, which includes several alternative magic systems, one of which would likely fit.
The other thing to consider with humans and the supernatural is Faith. Humans can use Faith to call on their God(s) for assistance, ranging from a boost to a skill attempt, to curing disease, to direct and flashy divine intervention (column of fire, parting seas, etc). You'd probably want to cut off the list at some point, either leaving out the more powerful forms of aid or leaving out the weaker ones. Dropping it entirely is another option, but I'd be loath to do that.
