I agree with your main point, I think, but c and pi are different. c has a unit and so can take any numerical value under a compensating choice of units. Pi is

I agree with your main point, I think, but c and pi are different. c has a unit and so can take any numerical value under a compensating choice of units. Pi is unitless, however, and cannot be defined as any other value. C and pi are similar also: c would be different, if the universe's geometry where scaled differently, even if meters and seconds were unchanged in transition to the alternate universe (assuming one can formalize what I am saying in a sensible way). Likewise, pi (circumference divided by diameter) would take a different value (or not even be a constant) in an alternate (non-Euclidean) geometry (assuming that a circle could still be defined there, which is more obviously possible than the c/spacetime hypothetical)