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Odds are pretty good that your Keen's don't have a stiff enough shank (aka insert) in the boot and this is allowing your foot and ankle to roll when side hilling. I prefer a trekking/mountaineering style boot for steep country side hilling. Think something along the lines of a Crispi Idaho, Lowa Ranger, TiCam, Camino, or Tibet. I wear the Rangers in some very steep country and they serve me well. Boot construction will affect lateral support much more than a taller boot will. I'd take an 8" trekker/mountaineering boot anyday over a taller boot that doesn't have the footbed support.
While guiding for sheep in Alaska it was the same. Most guys didn't have mountaineering boots and their ankles/feet would be hurting after a few hours. Lots of good boots out there now days. Zamberlans seem to fit me pretty good. I would go to REI where you can try on a few different pairs to see what you like. Regards, Branden