Here's plan "B". Hike up to the Perch on Saturday. From there you can go directly to Edmonds Col and take 2-3 hours off the time to hike to Nauman vs the Valley Way tent site.
Given the time of year, this would be a prudent thing to do. Surely it's worth the $10 for the convenience, if the caretaker comes around to collect. Plus there will be brand new tent platforms there.
The best way to get to the Perch from the road is to take Lowes Path to Randolph Path, and then jog over to the Perch. Budget at least 4 hours to get to the Perch. There's one long, steep climb involved on Lowes which I nick name "the killer half mile". The Lowes path trail head is across the street from Lowe's Gas station, about 3 miles west of the Appalachia parking lot - the one with cars parked 1/4 mile along the side of the highway.
The Israel ridge trail looks shorter and more direct (and it is), but it's a black diamond in terms of difficulty. There are a couple of tricky stream crossings on the Israel Ridge to make it more exciting and you may encounter high water.
Hum, if your heading up on a Saturday and the weather is nice, there will be a lot of people at these campsites on Sat night.