There is a better fix than this one, which becomes a procedural nightmare when it comes to arguing what is contiguous and what is not. It is to invest in the Speaker and the President of the Senate the power to divide bills into pieces (I call it a "caedo" from the Latin root "caedere," "to cut off or divide" as with a sword), thus separating contentious elements from those upon which all are generally agreed. The process allows the Presidential veto to be much more discriminating. The beauty of this idea is that it is doable as a rule change, not requiring a Constitutional Amendment.
If you're in the business of suggesting amendments, why not fix the Supremacy clause as regards treaties and the Article II provision for ratification instead? Those are much more critical changes than what you are proposing here.
There’s reason for you receiving no response?