Julius,
I gave up trying the stuff in Apple's FAQ; they accomlished nothing. Instead, I did the following:
1. In Contacts on the Mac, I used the export under files to do two things:
A. Exported an archive of my contacts on the Mac
B. Exported a Vcard version of the contacts to a file on the desktop.
2. I turned off the iCloud feature of the contacts on the iPhone and let the data delete
3. After those actions I signed onto iCloud.com and went to the contact list, selected all the contacts and then deleted them using that action in the little gear thing in the lower left corner. Then I signed off iCloud.com.
4. I signed back into iCloud.com and went to the contact list, which was now blank. I used the import function in that little gear thing to import the vCards from my desktop.
5. Then I turned on the iCloud feature on the iPhone. These steps took a little bit of time, because I have about 2,400 contacts including the comments and notes.
So far, there have been no difficulties and the lists synced. If it doesn't work, at least you have a set of contacts in the vCards and archive exported to the Mac to use to restore the list. I am having difficulties with duplicates, and I think that follows from residual list of contacts that is on the iPad; I am going to delete the contacts their and then run the duplicate function again. So I think the better practice is to turn off the iCloud on all devices, if you have more than one. On the Mac, this makes you create a copy on the Mac, which is what I wish I did, to scan for duplicates and get one, pristine version of the database before uploading the vCards to iCloud. You might want to consider that.
I have been dissapointed with Apple's apparent lack of understanding about their own product and the wierd behavior it exhibits.
I hope you make the backups first and then...best of luck and good wishes.
Mark
