The Republic of Cyprus, the only subject of international law on the island, cannot be excluded from its rights on its EEZ merely because Turkey is not a party to the Law of the Sea Convention. In any event, even if that was the case, Cyprus still inherently maintains its rights on its Continental Shelf. These ipso facto rights are rightly exercised by Cyprus and Turkey cannot raise any valid claims to the contrary.
The same stands for the unfounded argumentation on the rights of the Turkish Cypriots under the 1960 Constitution. Turkey cannot possibly validly claim that the actions of the Republic of Cyprus are detrimental to the rights of the T/C community as it was Turkey who attempted to dissolve the Republic by the 1974 invasion. And the T/C themselves cannot possibly argue that they represent in any manner even partially the Republic of Cyprus (see the numerous UN Security Council resolutions on this since 1963).
In any event, if Turkey is so confident about the validity of any of its claims why don't they refer these matters to the ICJ (International Court of Justice). I am sure you know that among jurists, it is undisputed that Turkey is attempting to flex muscles in order to terrorize the weaker powers in the region to share with her what would be entirely theirs. However, this is exactly why International Law is there: to safeguard that the strong will not impose his will on the powerless. This is the beauty of justice: Law is what separates civilized societies from a jungle. In my view, Turkey is desperately trying to justify its actions by inventing far fetched theories on "equitable rights", which I am afraid fall entirely beyond the letter and the spirit of the Law of the Sea as this was developed by the practice of the civilized nations (including Turkey itself as you rightly point out in your article) as well as by the Law of the Sea Convention the ratification of which (by the way) constitutes a prerequisite for any country who is aspiring to become an EU member.
Lastly, I feel that the sooner Turkey faces the realities of its actions vis a vis Cyprus and proceeds to put things right, the sooner it would be freed to achieve its great destiny and potential. It's only fair to point out that my views are biassed as I am a Cypriot living on a daily basis the consequences of the invasion and occupation of my country by a foreign military power.