Beside a correct extension there is a major reason for this kind of unsharpness in the corners with such an extreme wideangle:
Rectilinear wideangles can only focus on a flat image (like on land, flat objects). But your dome produces a virtual image, which is a spherical curvature.
So you cannot focus on center and edges simultaneosly with a rectilinear lens.
The curvature of the fild virtually appears to be stronger when the virtual image is closer to the dome. A large dome radius moves the virtual image more far away (~ 3 times the radius = distance from dome) and the DOF has a chance to cover becuase it becomes just next to infinity.
This is why big domes can compensate this error more than smaller ones can. Stopping down of course helps to get the corners within DOF. Remember: The center is the farest point of your virtual image. Maybe intended frontfocus combined with DOF could also help a little.
But no, I can not say something to the extension rings for this rig. Just a very sure reason for this problem beside the dome positioning.
by the way, fisheyes do not suffer under this problem as they focus on a spehrical image, not a flat object like rectilinear wideangles.
Julian