I apologize for the double post, but given that the problem has been solved on my end after a rather long back-and-forth between the AskPlaystation_UK Twittter account and the UK and Croatian call centers, I would like to share in detail what I have done and what fixed it for me in the end, in case anyone has the issue now and for future reference in case anybody needs to search for it easier!
WHAT WAS THE PROBLEM?
When I went under ACCOUNT MANAGEMENT-->LINK WITH OTHER SERVICES, I was hit with the error CE-35327, so I was unable to even reach the menu to link or unlink other services. The same thing happens when selecting LINK WITH OTHER SERVICES after pressing the SHARE button.
TROUBLESHOOTING DONE:
1. I have attempted to upload photos and videos using the SHARE button to the accounts currently linked, in order to test the connection - Photos and videos were uploaded successfully.
2. I waited for a few days as it might have been a temporary issue, even though the PSN status doesn't show any problems.
3. After waiting a few days, I have reset my Modem to Factory Settings, connected my Router to the PS4 using a LAN cable (perfect connection, 400/100 Mbps). No result.
4, Through the PS4 safe mode, I have then restored settings and rebuilt the database. No result.
5. I contacted customer support through phone and we attempted to restore my old PSN ID, in case the conflict was due to that. Did not help. No other practical solutions were recommended.
6. After speaking with their Twitter representative, I have tried to access LINK WITH OTHER SERVICES through a different account and one that I created on the spot - same problem in all of them.
7. Again by their advice, I have Initialized the PS4 with firmware 6.72 attached in a USB stick. Same result.
8. After contacting our phone support again, they recommended entering the 8.8.8.8 and 8.8.4.4 DNS sequences and to open several UDP and TCP ports on the router (will share this if you want to PM me).
No change.
9. Finally, I tried connecting the PS4 to a completely different network and network provider. Same result.
SOLUTION:
After another RESTORE TO DEFAULTS option through Safe Mode, I selected the RESTORE LICENCES under ACCOUNT MANAGEMENT. I now have full access to the menu and have successfully unlinked and relinked my accounts.
Cheers to the patience of the support crew!