timelapse - How to deal with large exposure shifts during time lapse?

First - I've 30 yrs shooting experience.

Not a novice. But, total Newbie to Time-lapse.

Just did my first couple of tests yesterday. My wife was shopping - had to occupy myself....
I kept them short just to practice the technique
5 min shoot time/ 1 shot/sec for 300 frames
D800/24~70mm @ 24/ .9 ND filter so I could shoot at slower shutter speed - 1/40th sec midafternoon (May 12 ~2:20pm) Beautiful big fluffy clouds & blue sky.

Here's the problem- when the sun was direct on the scene it was probably a good 2 stops brighter than when totally behind the clouds.
So if I make the sunny parts look good, the shady parts looked pretty dull & dark.
Trying to go in between made the overall scene low contrast with neither the full sun or full cloudy looking good.

I also realize that doing a dusk shot to night or sunrise the change will be smoother and more gradual than fast moving clouds midday - but I'm sure this problem will come up & need to know how to deal with it.

I did a test with RAW files and one with JPGs. The first one Im working on is from the JPGs, adjusted in Lightroomm 4.
Realizing that the files from the RAW will be much better - but I want to get the general technique down before spending that much time on another test.

Looking at it again, it's not too bad. In Lightroom I selected sequences of the "Cloudy" parts & bumped up the exposure & contrast a bit, and did similar adjustments to the full sun parts. But I think it can be better. I'm used to final still images from RAW that look great in both Highlights and shadows - not a moving image going back & forth.
http://www.jeffellisphoto.com/clients/Ulta_TmLpsScene2_24fps-2web.mp4

Dynamic range isn't the problem, but even in a short (10 sec) Time-lapse, due to moving clouds there were large parts of each - nearly full sun and nearly completely "cloudy". Everyone seems to feel that totally manual is the best quality (no flicker) look, but how does one deal with large alternating light shifts as opposed to a gradual change in one direction?