Why not claim that none of the fundamental constants of nature are in fact constant over time?

You asked for it :) "The fundamental constants—the speed of light, Planck’s constant, the charge of the electron, etc.—are taken to be fixed in value. But there is no theory to explain the fundamental constants, nor is there a reason for them to be constant. They could have been different in the past, and they may be different in the future."

The evidence begins to mount!