The trail from my trip report for Taum Sauk is, as Alan said, closed.
The trail i reported on from the Green Bench trailhead to the top of Magazine i assume is open. It's a steep and pleasant couple of hours to the top, passing some rock formations with bouldering possibilities.
I believe everything around Driskill is private, hunting land, or both. I've never heard of any reasonable, let alone desirable, route other than the dirt road / trail from the church.