..
Sorry for the drift, OP, but to reiterate what others have said, please seriously consider a NOBO JMT effort starting from an alternate place, like Cottonwood lakes. Permits should be easy-peasy, and Starvin Marvin has laid out an excellent overall itinerary for staving off any altitude acclimation issues.
..
Anyway, Salty, we had 19 days allocated to do the 220 SHR miles (in fact doing 190 miles in 16 days), kind of rushed us a time or two, I think 21 days would be more like it as some days, lots of days in fact we hiked 9 hours to do.... 9-10 miles. Other days we did 14-15 or so. Tough terrain! And time lost for route finding. We did find some use trails here and there to make the going easier at times. We also benefitted greatly from lots of leftover snow (in mid September!) on the down-side (mostly northern sides) of many of the tougher passes, where we boot-skied or glissaded in lieu of more rock/talus hopping. If I were to do it again, and we might, I'd go earlier for more snow terrain help and we'd bring an ice axe and microspikes. Go light! I can't imagine doing this "hike" with more than about 20 pounds on my back.