HELP! Eames Shell Chair Base Removal  

My first move would be WD40.
Turn the chair upside down and flood the screw holes with it, wait 10 minutes, then try unscrewing again. (Perhaps pulling "up" on the screw, to brace the nut against the shell slightly since it's now spinning, thus letting the threads unscrew)

Thanks william-holden-caulfield, but...
I tried it but did not work well. The other 2 screws that seemed to be OK are now loose, too, so now all 4 scres are freely spinning and going nowhere!!
I also noticed some cracks at the base/shell attachment loctions. There are supposed to be washers in between the shell and the base, but I guess the previous owner did not put any. It's a shame since the upholstery is in great shape and the shell is relatively clean except for these cracks.
I will probably have to cut off the pieces of shell to remove the screws & base, then put shock mounts over the openings to cover them up and to install the base...

Is it absolutely necessary that you remove the base?
Why're you trying to do this-- to clean the shell?

Yes...
I want to remove the base because:
1. I want to replace with another type of base.
2. Now that I see some cracks on the shell, I need to try to repair it.
3. I already started working on it, and I can't go back! (the screws won't get tightened either...)
Do you know what kind of nuts are used on the shell chair? I hope it's a regular size, so the damage to the shell is minimum even if I try to pull it out.

screwed
Unfortunately, once the insert starts spinning, it's nearly impossible to remove the screw by normal means The threaded insert is held in place with only an interference fit to the shell.
Sometimes you can wedge a wooden shim or a screwdriver blade between the base and shell. This will increase the friction between the insert and shell. Then instead of a screwdriver, use a ratchet on the screw so that you can give it a good snap.
I've had varying degrees of success. Good luck.

Thanks poach
I tried to wedge something between the shell and base, but I can't get a good grip of the insert...
I think now I have to cut the shell to remove the inserts out, or to glue everything so that they don't come off, ever.
Again, if I were to cut out the shell, how big do I have to cut so that I can pull out the insert?

I just removed it
I did it the hard way, by digging the fiberglass to remove the insert... The screws were badly rusted, no wonder WD40 was not very effective.
Thank you all for sharing your ideas & experiences! I might post some pictures later, to show my experince!