I haven't looked into those yet. If they can properly handle what looks like a 1½ second peak-to-peak (dim-to-bright or bright-to-dim) variation, that would be great.
Another thought would be to try the free DaVinci Resolve Lite program (in another system -- the one I'm using can't handle it), noted back in the Song Of The South thread, for it's luminance stabilization.
Since it is cyclical, I might try a 36-frame manual adjustment (and reversed) repeated across the timeline. Hmmm ...