You make an interesting case...but history is replete with examples of Representatives & Senators going to court only to get tossed on the basis of separation of powers. I would not get my hopes up. The only thing I see breaking this log-jam is the 'nuclear option' that's been suggested.
I don't think in this case that it is your standard run of the mill separation of powers issue. In this case both the it is not necessarily the executive "branch" vs. the legislative "branch" We are dealing with the explicit authority of the president to make nominations and the explicit DUTY of the Senate to advise and consent. Thus I believe that the constitution does not give the Senate the option of sitting on a nomination, but the Senate would be required to act upon that nomination. My guess is that if the SCOTUS takes the issue, the SCOTUS will interpret that clause to mean that the Senate cannot close its term without ruling on the nominations within that term -- since in essense there is a new Senate elected every 2 years. That would put an end to all the Borkings. That's for sure.
This is really a double edged sword. If the SCOTUS agrees with my interpretation, then a lame duck president could conceivably stack the courts by requesting that all the old dying judges that agree with his philosophy resign and allow the lame duck president to stack the courts with young ideolouges.
Nevertheless, I believe that this one has merit. I don't think it has been tried before only because nobody has ever used the filibuster technique to stop judicial nominations before. Now this issue is ripe for a SCOTUS review. Eventually neither side will like what happens.