The y_* files are actually 5D: dimx * dimy * dimz * 1 * 3. It is done this way because the NIfTI specification says that the 4th dimension of a multi-dimensional volume should be time.
Visualising anything other than the first volume using SPM is a bit tricky, but it is possible. If you try CheckReg, you can elect the first volume and then hit the edit button to allow you to give filenames of the other two volumes. eg.
/blah/blah/y_blah.nii,1,1
/blah/blah/y_blah.nii,1,2
/blah/blah/y_blah.nii,1,3
The Deformations utility should pretty much do what you want. You'd use the pullback to bring an image from time 1 into the average space, which should be relatively straightforward.
Best regards,
-John