So I got myself what has to be the nerdiest bluetooth keyboard in the world: http://sinclair.recreatedzxspectrum.com/
Quite expensive too, for a bluetooth keyboard. But build-wise, it's a perfect replica of the ZX Spectrum we know and love. Feels exactly right and has the correct key labels. Which means that used with a decent emulator, it recreates the feeling of typing on a real Speccy (without resorting to blind hunt-and-peck which is generally the case if you use a PC keyboard).
And after some fiddling with figuring out how to unlock the full bluetooth QWERTY mode as well as the Speccy-specific mapping, I can confirm that it works as advertised as a generic keyboard for Android, iOS or Windows.
I only had to ask myself, "can I think of anyone who's a more suitable target for this product" to realize that I really had to get it.
Now if they could only launch the full version of that Android app that was promised...