The one-handed music of Godowsky has its precedents too, and it's only appropriate that it would have been another of the 'composer-pianists', Alkan, who got in there first (there are examples by Czerny prior to Alkan, apparently, but his studies don't really count). His grand etudes, op.76, feature two studies, one for each of the hands on its own, followed by a study for both hands in single note unison. These are pretty damn rare, recorded only a handful of times (including Hamelin, of course), but there's a sparkling little connection that is worth noting. The Grande Etudes were written by Alkan between 1838 and 1840, which coincide with the writing of (Alkan's good friend) Chopin's 2nd sonata, which features a finale written in, of course, single note unison. It's fair to say that they would have known what each other was up to.
This is Rachmaninoff playing the Chopin finale.
And here is a strangely frat-boy rendition of the Alkan, with a false start. (skip to 1:27 to avoid)
Besides the similarities, the Chopin is far more accomplished, as you'd imagine, with a less anchored tonality and a greater dynamic range and scope for rubato, but the Alkan is definitely worth a listen, diabolical and olympian at the same time.