The solution of the problem is a 4 way process. It does not depend solely on Turkey but on the other 4 sides. Even If Turkey show willingness to solve the problem the problem can not be solved as long as the other 3 sides do not show willingness or good motives to compromise to arrive at a REALISTIC solution.
I believe that Turkey at the last negotiations showed a desire to solve the problem. You have wrongly interpreted the UN plan as a partition plan.Moving from an independent state to the UN plan is a significant change !
If Turkey did not want to solve the problem it would very clearly reject to negotiate. You can not always accuse Turkey and on the other hand fail to observe the wrongdoings of other sides! Turkey had make many compromises to change her attitude from a complete independent state to the UN plan.
I would go further and say that the COST That you are referring to be expanded to cover the other 3 sides if we expect a solution soon and not far far in the long term.
Regarding the North Ireland statues this is not an international dispute or problem as it is the case in cyprus.