Many times I have seen wood shingles removed, the roof decked, and new roofing installed ... and homeowners saw an increase in energy bills. That was largely because they neglected to add ventilation (both intake and exhaust) to the attic during the process. I know that Decra has also worked some with radiant barriers beneath their battens and that seems helpful as well.
I doubt you will find a direct study that will reference your exact scenario to assist in the justification of that application.
Are they paying for the complete replacement of a cedar roof?
Usually if you are dotting all your "i"s and crossing your "t"s, you have a decent amount of money in the project to cover the full replacement and perhaps the incorporation of some additional insulation or cross batten design for air flow. Add in some radiant barrier and you have a great combination for rejection of heat from the roof assembly.
I read the Decra website study by the Oakkridge national laboratory. I'm just a homeowner but it seems that the study says counter batten installation helps remove about 30% of the heat in summer.
http://www.decra.com/technical/sustainable-roofing
It appears to show asphalt injects the most heat into the house 45000 BTU/ sq ft/ day, stone coated steel on various installs, 2k to 3K/ btu/ sq ft and stone coated steel over a cedar shake roof only 1100 BTU Day. The Cool Roof Council rates now banned cedar roofs as one of the roofs that put the least energy into the home.
Does anybody know of any research or build plans that can cut the amount of energy a stone coated steel roof injects down to the level of a cedar roof. If I can find a credible tested plan or research, I could use that to justify building it to my insurance company because they will pay for items proven to be necessary to make the replacment roof perform in a like kind ( AC cost) roof. The reason I need a proven documented source insurance companies won't accept anything unless it's documented research or from an engineers wet stamp plan.
For those coming to this thread, the merits of various roof deck insulation are a much debated an analyzed topic over at Green Building Advisor. Building Science Corporation has also done a ton of work on them.
Cool roof designs (ventilated ones) are a hotly debated topic over at Green Building Advisor, https://www.greenbuildingadvisor.com/
And sometimes tested by Building Science Corporation for commercial clients.
These might be good resources for you.