I enjoyed riding the Push Mtn. road, but like Old Guy, I had trouble tying it into a riding loop, with overall far better riding west of there. I ended up just riding 412 back toward Harrison and into the Ozarks.
The roads in Arkansas are incredible, grip wise. On one tour, it rained a couple of days straight and after settling in and accepting the fact that it was going to be wet, I started to lean the bike over more. I found the grip to be fantastic - but I do agree that it eats tires. Guess you can't have that both ways.
From the north end, Hwy 5 south is pretty good. Then you can take 56 east over to 9 and south into Melbourne. Then that section of 9 to Mountain View is a hoot!
We decided a long time ago that Arkansas roads are tough on tires. It makes planning for tours tough trying to figure out whether I can go for a ride and still have enough tire for an upcoming tour. I had a spare rear wheel for the Goldwing, and that helped. No spares for the FJR, though.