Foam Board usage in Cathedral Ceiling

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I'm trying to make a bedroom out of the upstairs attic space in our 50-yr. old house, which has been finished off by previous owners. There is practically NO insulation, but what I was trying to do was get a high R-value between the ceiling and the roof, where there is currently a 6" space with some kind of kraft-faced insulation (I'm guessing R-13).

I calculated that I could get an R-30 with several sheets of 1/2" foam board (leaving a 1" gap for air), but don't know if that's feasible or not; I plan to install a ridge vent and drip edge vents (as there are only gable vents now) to add ventilation, as it gets really hot and humid in Greenville, SC!

I also wanted to install a radiant barrier, but don't know if I can squeeze this between the sheathing and rafter vents; any help would be greatly appreciated!