I must be drunk or blind, or drunk. I saw "supermoto" pavement stuck in my head. In my experience, Old Maverick Road is an excellent piece of starter gravel and connects to both some lovely scenery and the fun to ride Ross Maxwell scenic drive. The short bit of gravel leading to the Hot Springs isn't much but the hot springs are. The River Road, from the East, is fun and easy for several miles and you can simply turn around when you start thinking it's a bit more rugged than you'd like. The roads all change as they get graded every so often, and the rangers will be able to tell you whether they've been washed out or not.
There's plenty of good gravel in the park, but it's good to not ride alone on a big bike because get-offs do happen..
Cannonshot's documentation of the area is very good, and the park maps are excellent as well.