This

... I don't feel it's in any way meaningful ...

is an intrinsic feature of the problem, because to be able to express the visible range as a fraction of the EM spectrum, you need a measure on the latter, and there is no natural way to do this.

The closest you can get is to assign a measure that is uniform in logarithmic scale, with long- and short-wavelength cutoffs at the size of the universe and at the Planck energy, but that essentially implies that there is an equal amount of interesting phenomena happening at photon energies vastly larger than anything than we've ever had access to, as in the ranges where we do have access, as well as a large almost-bottomless well of wavelengths that don't even fit inside our own galaxy. Physics, of course, doesn't care ─ but we, as humans, do.

All of which is to say: there is no unique answer that comes from physics. If you want an answer that's relevant to humans, then you should base your measure on cutoffs which come from human considerations. I would personally go with a logarithmically uniform measure with cutoffs at about ${\sim}10\:\rm TeV$ (about the highest energies we can reach in particle accelerators, hence about the highest gamma photon energies we can control) and at about ${\sim}1:\rm Hz$ (from the ELF radio band). But, again, that's ultimately a subjective choice.