mine's a single speed hard tail that will probably have a rigid front by then and i'm gonna go for it!
What's the longest ride you've done on that?
I ask because consider that it will be 3 back-to-back-to-back >45 mile days. Takes me about a total of 24 hours of actual cycling to ride it, usually about 7, 10 and 7 hours days when stopping for lunch and sightseeing. That assumes decent weather.
The first day would be fairly short distance (if you skip Western Rim, about 30 miles) but Mary's Loop to Rabbit Valley is a fairly technical ride. With Western Rim (which I highly recommend), it's about 42 miles.
Depending on the schedule, the second day will be about 60 miles total (you can bypass Yellow Jacket to cut off about 6 miles) with the Dewey to Top of the World climb (6 miles, 1500'). There are some very long flat sections where you are spun out in big ring out near Cisco, too.
The last day would be 45 miles long with about 20 miles and 4500' of climbing total. If you do Porcupine, then it's also a pretty technical day. If not, going down Sand Flats, then it would mostly just smooth roads. Could add Slickrock in that case, though.
I am not discouraging you, plenty of people do it on rigid one speeds, but gears and squish might make it less of a death march. Don't misunderstand, I've done 18 hour races and Jeffco trails on my singlespeed. No way my knees and back would take Kokopelli on it, though (and it has a front shock!).