Would you consider flash with high speed synch, and a better beamer? This is a difficult scenario indeed.
You could get lower to the ground and use the sky as a giant White seamless. I've used that many times before.
With flat light I sometimes use split toning in LR4. On your pic I gave highlights a yellow cast and shadows a blue cast. I also cranked the clarity slider up to 70, darkened the sky and added a blue cast, turned down the green and yellow channels and added some vignetting. It probably took 5 min. Clearly all these things can be done with the software you have but maybe not as quickly.