When I play BW the GM is someone who is a longtime player in my group (though also the newest RPGer among us in that he began in the late 90s rather than early-to-mid 80s) but has only ever GMed BW.Burning Wheel is close, but much like how Fourth Edition's skill challenges can obviate time and place Versus tests and intent based resolution combined with Let It Ride have a similar impact where they are less about specificity of the fiction and more broad strokes.
I think he is better than me at the time/place aspect you mention. I think my BW leans closer to 4e/Cortex+ Heroic in the sort of way you don't like so much.
Oddly enough I think that Prince Valiant might be helping me develop that aspect of my GMing. I'm not sure if I can quite explain why - maybe because it defaults to painting in such bright lines and crisp colours that it makes it easier for someone for whom it's not first nature? As a GM I tend to lean into the emotional/stakes side of the situation rather than the time-and-place. (This is why taunting the players is such an integral part of my approach!, and why I don't do well with systems that would make such taunting mean-spirited or adversarial eg B/X.)