From the pic it looks like you are making the walls kind of thin. I suggest making the disk at the equator solid with just a small hole ~0.75" or so thru the center, put the same hole thru the polar disks. Then when putting it together glue a hardwood dowel in those holes, leave it long and use it as the axis for spinning the sphere. Cut it off flush when done and cover with the final polar disks if you want to hide the end grain, you would have to shape them by hand or with some different setup.
That will make the sphere a lot stronger, thin sections of MFD like you have tend to come apart.
As far as turning it, low RPMs is the nature of larger diameters I would start at about 10 RPM and see how it goes, a variable speed motor is real nice for this type of thing.
You may want to consider doing the initial roughing with something like this, rather then the router.
Could just do it by hand as the sphere spins and check with a template as you get close. Then just do a finish pass with the router.
Rig up some kind of power feed for the router then the slow speed is not as much of a problem.