The Constitution is pretty much only as strong as the institutions that interpret and enforce it. It's all sort of a collective hallucination that the Constitution has any power in and of itself. "Godelian" defects seem a lot less dangerous to me than plain-old human factors.

The UK manages to be a Parliamentary democracy without having a single coherent constitution at all, let alone one free of logical defects- so having a perfectly consistent and "loophole-free" constitution doesn't seem particularly important in practice.

The easiest way to wholly undermine the US Constitution is to just expand the Supreme Court bench and then pack it with your cronies, who will then let you do whatever you want and call it constitutional. No amendment needed!