It's important to note, that a split keyboard doesn't make all that much sense without touch typing, and touch typing didn't exist until 1880s and wasn't widely recognized until WWI or so. Furthermore, there were many competing designs at the time, ranging from completely different "index typewriters", to huge-keyboard typewriters (such as Caligraph), to Sholes/Remington, to keyboard typewriters designed for touch typing (e.g., Blickenderfer or Typo)—those even had curved keyboards in some cases (see, for instance, the
Typo).
The oldest truly split keyboard, that I'm aware of, was patented by Heidner in 1915 (see
US Patent 1,138,474), and the first published experimental research was by Klockenberg in 1926:
KLOCKENBERG, ERICH A. (1926): Rationalisierung der Schreibmaschine und ihrer Bedienung. Psychotechnische Arbeitsstudien. Berlin: Springer.