Ok without pics this will be hard to describe but here is what I would do.
1 - Cut the underlying board (the mount) the same shape as the fiberglass pedestal
that is there. However extend the mount beyond the pedestal enough so that the head can be rotated (about 45 degrees) in the space. The front end of the board will have a parallel angle to the front end of the underlying pedestal
2 - The head will now be mounted diagonally in the space.
3 - If required for stability and support at the front end of the mount extend legs or even a full front facia extending to the sole to support the front end of the head.
I am pretty sure I have the same head with the compact bowl. It might fit your needs a little better but the limiting item you have right now is the mount and I think that is the same - i.e. the compact bowl doesn't have a more compact mount.