As you've probably found out already, seclusion doesn't come cheap on Paxos
Planos have some nice properties that are probably within your price range and worth looking at http://www.planos.co.uk/ Or if you want to splash out a bit more, Greek Islands Club have some really nice places and their service is excellent. Two of their places which I've stayed in are House of Athena - VERY secluded - and Daphne Villas, which is a pair of villas, far enough apart from each other to be fairly private, but far enough from anything else to be really secluded.
CV Travel also have some really nice properties that I'd put in the honeymoon class. I've never stayed at any of them myself, but I do know that CV are a very long-established company with an excellent reputation, so I wouldn't have any hesitation in recommending them.
Hope this helps and congratulations on your forthcoming marriage