(Presuming a start line at camp ~.5 mile south of 89a on FS 205 (approximate mileage in bold). Full route adds up around 130 miles, with a smidge less than 15,000' of climbing.)
Start on 205, stay right through 2 intersections on 634 for 2.5.
Cross 67, continue straight on 461 for 5.5.
Merge (R) onto 462, downhill for 3.
Left on 22 for 3.5.
Right on 423, go 5.
423 ends, stay straight on 427 for 11.
T intersection, turn right on 425, go 3.5.
425 becomes 292, turn left (on 425).
Go 2.5, staying right on 425, then bear right on 272a.
Go 2, uphill, on 272a.
Turn left on 272, go .5.
Right on 250, go 1.5.
Right on 214, go 3.5 to start of Rainbow Rim trail.
Follow RR for 18.
Straight off RR onto 271, 8 up hill.
Right on 206*, go .2.
Bear left onto 222 for 5.
Left on 270 for 1.
Right on 22, go 2 to 67.**
Straight through on 611, go 1.
Right on 610, go 5.
AZT singletrack on left, go 12 on signed AZT/trail 101.
Right on 213***, go 5-6.
Left on 220, go 12.
Left on 224, uphill (!!) for 3-4.
Left on 205, go .5ish, look for AZT TH on left.
Right**** (north) on AZT, go 9.
Turn left on 205, go .5ish to finish.*****
*This is the second time you'll see 206. Pay attention to the map.
**The Kaibab Country Store is a ~mile up the pavement to the north. Recommended resupply, bring cash.
***There's a trail sign on the side of the singletrack (in a nice aspen grove) right before the road crossing. Pay attention.
****The AZT is faint and overgrown for the first three miles, but signed. Be careful, especially if it's late.
*****Following the AZT back to the actual TH is confusing as hell in the last mile(s). Following the two track of least resistance seems to lead right back to camp. Or, snag a gravel road and head downhill. It doesn't matter, just make sure you take the same route as the person against whom you're sprinting.