The closest I got: Jackals. It's got only religious magics, it's a variant of OpenQuest (but is not similarly open... Grumble.) That the casters tend to be doing almost as much DPR as the tanks... and much of that from melee weapons... 6 sessions down. More to come.
It feel less like howard or vance, and a bit more like The Books of Judges, Ruth, 1st/2nd Samuel, 1st Kings... with occasional bits of other, earlier, works in that most common anthology called The Bible... The Luathi are explicitly a pastiche of proto–Canaanite and proto–Israelite; the existence of both Kings and Judges makes it mostly cognate to 2nd Samuel.
But it does have fantasy monsters to kill, and killing them my players have been in the last month and a half. And clergy can work magics. (All magic is religious.)
Runner up? Dragonbane. Did not go well. I like the system, but the adventure was WAY too lethal.