The 2nd major dirt road running N-S is Baylor Canyon Rd.
I would highly recommend starting from the paved Dripping Springs parking, if you can live with the time restrictions; i.e., the parking doesn't open till 8AM, and closes at 5PM October through March (7PM April through Sept.). The trail from Dripping Springs meets the trail by Modoc Mine at 6400', about 1.8 miles in, and has fewer gratuitous ups and downs. A reasonably conditioned person can do this RT in about 6 hours, provided the weather cooperates. A bold driver of a burly 4x4 can get high up on the Modoc Mine Road, but as of 2015, that is a rough road, and most will choose to park by 5400'.