That 13.8 billion light years isn't a constant of the universe. It's a temporary condition, an accident of the particular instant in which you happen to be looking. There's nothing fundamental about it, so the fact that you got it out of an arbitrary arrangement of other values is a coincidence.
I think this one stands out because it has to do with charge & gravity, and protons, electrons, & photons. Which are the stable & abundant "things" in the universe.
The number you've "predicted" is "the age of the universe", which isn't constant. Unless you can show why this particular instant in time is especially interesting, then it's just another number, no more interesting than any of the other numbers you generated in the process.
As in, taking the point of view of cosmology about 100 years ago, before the redshift was attributed to the Doppler effect. And before the notion of a big bang was the default basis of reasoning.
- What if H is just a measure of redshift? Literally just redshift. Not expansion. Not an age. Just photons losing energy. At a rate of H.
- What if H actually is constant? Like G and like h and like k (Coulomb's constant).
- What if the universe doesn't have an age?
^ not rhetorical questions. Actually asking.