Thanks for the compliment. But I gotta tell ya, the big black oval things ARE the upper strut mounts with the spherical bearings already in there. The underneath side of the strut mount has nuts welded into place. That is where the allen bolts in your picture are threaded into. The big nut on top simply holds the strut in place in the strut mount.
Maybe this pic will help.
From what I can tell, if you use the stock mount and try to put the new bearings in there, the collars for the strut bar will not fit the old mounts.
I have to agree with Erik.
If you insist on removing the rubber, unbolt the shock and push it into the fenderwell as described above. Leave the strut mount in place. Take a 2 ft pipe/bar that will fit the ID of the stock strut mount. Usually, you can work the bar towards the front of the car and walk/push out the rubber bushing into the fenderwell. This is easier that drilling, burning, attempting to clamp the mount into a vise, etc. Let the car hold the mount in place.
On the other hand, this is slightly entertaining, so if you end up not needing the old strut mounts after you push/cut the rubber out, let me know. I'll be happy to pay shipping if you are going to throw them away. No, really... I need them for another project.