I performed this bit of zanyness back in '01, South-North-South, as an 18-hr dayhike, using Bright Angel on the initial descent and return (48 mi). Doing the trip with a camp along the way would be a different game, of course (heavier, slower) although I'm not sure which approach you had in mind. (Also, South Kaibab is shorter but steeper than BA - not as much of an issue if starting on the North Rim, perhaps.)
FWIW, it was late October in '01, much cooler at that time of year, and I'd just come off 1000 miles on the PCT. Still, I walked, didn't run, and had no specific conditioning for any sort of record attempt (which I was not out to achieve). The R-R-R is, like thru-hiking for the conditioned thru-hiker, mostly an exercise in mental fortitude.