Looked like a great trip!
I tried to do Schnebly Hill Road last week. The section between the Merry Go Round and Vista Point lookout is closed for repair until later this month and then another section will be closed for repair till late August, I can't remember which section. The Forestry website says it's open and the ranger didn't tell me it was closed, I was planning to drive up it from Sedona and camp up the top but couldn't.
https://www.fs.usda.gov/detailfull/coconino/alerts-notices/?cid=stelprdb5339811
The road was rough and slow going but not difficult. I will go back up later in the year and finish off the rest of the trail and see what they have done.