Hi DutchDutch
I changed my EASA french licence into an Italian, time ago as the french refused to endorse a rating completed in Italy.
Straightforward, no big deal.
However you will have to transfer your medical records to the new state of issuance, and if I am not mistaken take the first medical there.
Good luck with dealing with the Greeks they need to send your medical over.
Then some countries like France will require proof of residency if you are not a french national to issue the new licence.
I know for sure the UK will issue you a licence without you needing to be a UK national or have residency there.
Check that out with Belgium, if you are a Belgian citizen, it should be OK.
Good luck !