There was an inefficiency in how the voxel-level ambient occlusion was fetching surrounding voxels via tetrahexacontree traversals to calculate ambient occlusion shading in the GLSL fragment shader for each ray voxel hit .  It still traverses the tetrahexacontree to fetch the surrounding voxels, but caches the voxel volume index for each traversal following the first traversal to a given volume.  So if all the surrounding voxels are within the same volume as the first traversal, only that one initial traversal is needed.  If one or more of the surrounding voxels are in other volumes, it caches those volume indices as well to avoiding additional traversals.

The same inefficiency was in how the voxel-volume-level ambient occlusion  fetched non-air voxel counts and was solved with the same voxel volume index caching mechanism.

In implementing this optimization, I realized the voxel-level ambient occlusion could also be sped up even more if I keep bits in each voxel indicating if a given voxel face (same x, y and/or z plane) and its surrounding face plane neighbors are air voxels.  If the surrounding voxels for a given face are all air voxels, then the face doesn't need to be shaded by voxel-level ambient occlusion.  I'm working on this and it should yield even greater performance gains than the voxel-level ambient occlusion optimizations described above yielded.