Couple of very similar posts today! I sing to the box, and if you 'lay out' a pavement of chords against a voice rather than try to play tune, the system doesn't matter so much. The issue is whether the chord voicings are there.
Have a play with
http://squeezebox.chrisryall.net/ which is still under development but up to this task. There is a B/C preset - but your basses may differ. Tips
1. Incomplete chords often work. The notes to sacrifice are tonic or 5th.
The other notes carry much more harmonic 'colour' and the 3/7 clash
is critical to the effect of a dominant chord
2. Sometimes a 'relative minor' works when the major is incomplete
3. If eg B doesn't work - look at Bb and C or even A and C#. Most people's
voices will take this degree of nudge and a B/C certainly will.
4. Try different 'voicings' - eg that tonic might sound nice at the top
Above all try things out on your own box - your ear is the best judge of what works and if in a chord run one of them is a 2 notes - the audience probably wont notice as the song will carry it. Good luck