Overlapping cascade? On the cell the cascades overlap each cascade only contributes half luminance, so you sum to your full normal luminance but get a halfway transition?
I'd been thinking about a paper where they voxelized static geometry for the scene, injected into the LPV grid, and used that as a means of secondary shadowing (i.e. don't transmit beyond a cell that's solid). Using that you could also create a Sparse Voxel Octree instead of a regular grid. Your cell sizes would get progressively larger, you'd have to less iterations to get light farther and use less memory, minimizing the need for cascades. But with the jump in quality differences I'm not sure how well that would work. And you'd get greatly varying amounts of light distance based on areas of scene complexity.
I'd also thought about something like LPV just transmitting anti-radiance. I.E. if you have a typical hemispherical light term you transmit the opposite of that to "block" it as a shadow. Voxelize the scene, iterate enough to transmit anti radiance (no color needed) a good enough ways, you'd get a nice realtime shadow term from your skylight. Not what you probably had in mind, but I'm just spewing ideas. The guys over at Crytek recently complained that there's no good solution to GI/Reflections and exhorted others to solve this problem, since they invented (and for Crysis 3 improved upon) LPV to begin with I assume they're just not happy with it, probably for much the same reason you're seeing now.