The story I've heard is that Davy started with "alumium", but added the "n" because the pronunciation was deemed too awkward, yielding "aluminum". Others pushed for "aluminium" because it sounded more consistent with other elements' names.
Unfortunately I can't edit my post; I would add that I am repeating a story I have heard---it is broadly the same as Wikipedia, as you point out. I am certainly not an authority!
https://en.wikipedia.org/wiki/Aluminium#Different_endings
The story I've heard is that Davy started with "alumium", but added the "n" because the pronunciation was deemed too awkward, yielding "aluminum". Others pushed for "aluminium" because it sounded more consistent with other elements' names.