That's a promising idea. I was wondering if there was a way of taking the bright clip and chopping out all information above 128 luma, taking the dark clip and chopping out all information above 128, and then simply adding them together.
Or maybe something slightly more sophisticated would be to do the above on the extremes (say, above 192 and below 64), and blending the center range.
Of course, there might be some strange effects I haven't considered. If there is a way of "chopping" above/below a certain luma with some small degree of fuzziness, that would probably reduce the possibility of artifacts.