I don't know if it's quite 17 miles that first day but it's fairly easy terrain. I'd seriously consider it. Live Oak Spring is well off the trail and hiking down to it and back up would not be worth just carrying the extra water. Can't really say much about Butterfly since I've never done it from that direction but all the other peaks are right off the trail. And if you don't bring 10 stoves to test, you should be able to do it even with full packs.
To stay at Fobes would make for a very short day. Cone Peak is a little involved but Palm View is nothing and doesn't really have a view. Spitler and Apache are right off the trail. Getting water up the Apple Canyon Divide would be easy. I figure a gallon or so each and I'd go through the Zen Center.
I'll talk to my father-in-law today and see if parking works. He might even shuttle you to the trail in his truck.
Hal
