When does the North Rim usually shut down for snowfall? I don’t know, but I’d look into it. October seems potentially on the edge of the season.
There are non-Uber drivers who advertise on every city’s Craigslist page. Maybe you could agree on terms in advance?
R2R has always struck me as one of the most extreme ratios of driving distance / hiking distance.
I’ve skipped the shuttle, permit and overnight gear by bouncing it in a day (R2R2R), but I was 1/3 my age then. I have seen senior BPLers in better shape than me do it, though, on a day I only went 30 miles.