Interesting question. I think the best way to find out might be a limited experiment with just a few plants since there is not likely any research on this, especially with daylilies. Just thinking "out loud" if one extrapolates from other plants, say turf grasses, then I'm not at all sure it would work. When turf is under heat and drought stress the recommendation is to increase the mowing height, not decrease it. Transpiration is the plants' cooling system.
Most plants respond to reduced foliage by growing new leaves to replace the reduction, but that might depend on how far back you cut. If that happens then they'd have to use stored carbs in order to regrow. My inclination would be to assume that the plants know what they're doing - going dormant is their way to avoid the stress and they determine when to do that.
Manipulating the watering schedule might be another option. What happens if you water less frequently but for longer? Another thing that is done for heat sensitive turf is "syringing", which is a very brief light watering of the foliage only, just enough to wet the leaves but not into the soil, to reduce the plants' temperature when it is very hot.
