There is a lot of precedent for successive Senate bodies abiding by the rules of previous Senates. They been doing it for about 200 years now. I don't think the Supreme Court would allow the Republicans to make up the rules as they go.
If we actually could legally change the rules then we will have to live with the consequences when rats or another party gain a majority and the "tyranny of the minority" is no longer available to stop them.
That's why I pointed out the "de facto" aspect of judicial confirmation. The Senate can put into existence any rules it wants to, but not if it causes a fundamental change in the actual number needed for confirmation, which the judicial filibuster clearly has. Any such rule can, and should, be ruled out of order by the chair, because it effectively amends the Constitutional requirement without an actual amendment passing.
Your point about breaking cloture is only partially correct, I believe. I may be mistaken here, but I believe all that is needed is for the Senate Majority leader to appeal to the chair (Dick Cheney) to rule the judicial filibuster out of order with regard to Senate rules, and that kicks in the rule where each cloture vote results in a diminishing majority needed to invoke cloture (57, then 54, then 51).
The question, IMHO, is not whether or not they can do it - they can. They have the votes.
The question is the 'Rat response. They threatened to completely shut down the Senate in the last Congress. Now, with a good hearty electoral splash of reality, including Tiny Tom enjoying retirement, you have to wonder how quick they will be to continue that threat.
You haven't been keeping up.
A point of order would be raised on the constitutionality of the filibuster in advise and consent. The chair would rule it unconstitutional. The ruling would be objected to by the Dims. The question of the ruling on the point of order would be put up to a simple majority vote as allowed under current rules. And assuming you hold at least 50 Republicans plus the Veep the filibuster rule changes on advice and consent.
The Supreme Court has exactly SQUAT to say about Senate rules. Furthermore no Senate can bind a future Senate, because the future Senate has exactly the same power to change a rule as the preceding Senate.
The Supreme court has no say in how the House or the Senate conducts their respective business.