Re chords and basses on B/Cs (Paul Burke) - some have 2 Cs and only one D, (the older variant) some have 2 Ds (and only one C) - the so-called modern arrangement: with these it IS possible to play at least some chords in tunes in D and G. I also have a stop to take out the middle third of any chord, so can use all the chords as major or minor, and do indeed make use of both A and E in this way. The one that's missing is a Bm chord, and I do play quite a few tunes in Bm, but that has to be all right hand only.
And I have also seen some Hohner B/C boxes with stradella bass, which seem to be much liked by their owners as being more versatile.