... do we know if Wheatstone, or any other English maker, ever managed to double up on reeds to get octaves or wet tuning, like a typical chemnitzer or bandoneon?
Yes, George Jones may have been the first, as he claimed to have in "1859 made the Celestial English and Anglo Concertina." (At the time "Celestial" was being used to describe a tremolo-tuned German concertina, and "Organ Tone" an octave-tuned one.)
As Chris has mentioned, Lachenal's produced a number of their "Accordeaphones" in the early 1930's, and even Wheatstone's made at least one triple-reeded concertina, an enormous MacCann duet that used to sit on top of Jim Harvey's sideboard (minus its reeds, which Tommy Williams had "cannibalised").
I would suspect that the 1931 "Accordion" Crabb concertina, which Geoff mentioned, may have been double-reeded, and certainly they custom-made a brightly coloured trio of double-reeded instruments in the '60's, here's a photo of the red one :
I have also seen one made by Colin Dipper, and I'm sure that there have been others ...