In the Stroke Palette, Under Curve Stroke Modifiers, is a "Curve Projection Range" slider that will control how much a curve will follow the underlying surface.
BUT
The Curve Strap Snap brush you're using create's simple, planar faces. This severe lack of vertices will not give these strap faces a lot of leeway to follow the surface underneath, so there will always be some clipping if the suface underneath is complex. I'll see if there is a curve brush with more vertices that can compensate to hug the surface better.... otherwise the topology brush might be a better tool to create a strap that truly hugs the surface.
Replies
BUT
The Curve Strap Snap brush you're using create's simple, planar faces. This severe lack of vertices will not give these strap faces a lot of leeway to follow the surface underneath, so there will always be some clipping if the suface underneath is complex. I'll see if there is a curve brush with more vertices that can compensate to hug the surface better.... otherwise the topology brush might be a better tool to create a strap that truly hugs the surface.