I also started thinking about how to present some of the green 10 key values in a way to appeal to moderate republicans. In the list of 10 key values there is "grassroots democracy", "decentralization", and "sustainability".
One of the platforms the current republican party has campaigned on is "smaller government" which seems to have appeal among Americans. Somehow NSA spying, the patriot act, non-competitive contracts to well connected businesses, and of course steadily increasing military spending, seems to be incompatible with the idea of "smaller government".
Decentralized democracy is about trying to push authority away from large centralized bureaucracies, that at least means the centralized bureaucracy should shrink.
Also I think a sustainable society should have a government that lives within its means. It seems like two of the conservative "revolutions", Regan and the current Bush, have been unmitigated disasters for the federal deficit.
I'm not sure how many greens would be behind the idea of fiscal responsibility. It is certainly seems compatible with the ten key values, and also might help broaden the green party's appeal.