John, I yield to no one in my respect for your constititutional knowledge, but I think you are wrong, for two reasons.
Reason one: The current number of votes needed for the Senate to consent to a nomination is 51. The rule of the majority which you seem to think exists in penumbras and emanations of the treaty clause is in effect.
Reason two: Article I, s.5 constitutionalizes ANY rule the Senate makes about its internal proceedings. If you think Rule XXII has ever been ruled on by a court, I would love the cite. I think its a nonjusticeable question, and I would be very surprised if any Federal court would entertain a challenge.
The argument I would make is that because Congress is under no obligation to pass or even consider legilsation, rules which prevent such action from being taken in a timely manner are fine. On the other hand, the 'advise and consent' role of the Senate is explicitly mandated. Any rule which by design prevents such role from being fulfilled in a timely manner must therefore be, at best, suspect.
That case hinged in part on the difference between a 2/3rds vote for treaties and a simple majority for other Senate decisions.
To prove the point that a Senate Rule cannot trump the Constitution itself, consider this: Senate Rule says, "No votes by women who happen to be Senators will be counted toward passing any legislation." Do you have the slightest doubt in such an instance that the Constitution governs, and the Rule would fall?
John / Billybob