Scott,
You will probably have a hard time believing this, but Bethpage is LESS impacted by weather than Shinnecock. It drains FAR better than any and all of the courses you mentioned because of its sandy base. That is why it was even remotely playable in 2009 after an entire MONTH of daily rains. It is that aspect that gets forgotten. In addition, heavy winds, as can happen also at Pebble and plagued the 2000 Open there can also affect Shinnecock and Sebonack.
Each venue has its own particular set of strengths and drawbacks; ALL are Open worthy and would make good choices... In fact, that is the problem with the idea of having a "rotation" of venues. Our country has far too many deserving courses, old and new, capable of and willing to host the national championship...