Hi PurpleCat! I don't know if I'am too late with my idea but this is the remedy I have found, although a bit delicate:
1- Go to applications
2- open disk utilitity
3- Make sure the FIRST AID is selected (because this is the delicate part) you could wipe your computer of everything you have in it.
4- Select the disk on left side and there will be 2 options at the bottom:
VERIFY DISK PERMISSION and REPAIR DISK PERMISSION
5- Click repair disk permission, and reparation will start inmediately
6- After everything is repaired, Restart your computer Almost sure, evercookie will be gone.
I'am still trying to find out if there's a way the computer can reject this kind of invasion of privacy.