I think that many people are overlooking the matter of available
techniques and materials in 1900 when supposing a computer operating
in the Kops range was possible.
No printed-circuitry; indeed, the mode of much electronic
construction was busbar-type wiring on a varnished piece of wood. I
don't know when enameled "magnet wire" came into production, but the
standard for magnet wire for a long time was silk covering. Hookup
wire may have been cotton or cambric, with gutta-percha for
insulation.
Resistors of any precision would likely have been wirewound.
Does one need audions for amplification? Consider early telegraph
repeaters or even chart recorders (running on a wind-up spring and
recording microvolts). Even audio amplification could be achieved
using compressed air.
At the time, pneumatics were at a pretty high stage of development.
Consider the workings of a player piano or pipe organ.
But I think the technology that would have been selected in 1900
would have been mechanical or electro-mechanical. Consider, for
example, the work of Leonardo Torres Quevedo.
Cheers,
Chuck