I prefer 'mills' (mBTC) and 'mikes' (uBTC), as it reuses existing patterns well-known to anyone who has had a need to handle numbers of anything over a range of magnitudes (i.e. the SI system, used nearly universally in other areas of measurement). I may be in the minority. As such, I recognize the need to sit back and let consensus emerge. Trying to force the issue will not be resistant to whatever socially-selected solution eventually emerges.
this is excellent! i have updated OP.
I like BITS because it sounds cool.
maybe we can have the best of both worlds by renaming these, mills (mBTC) bits (uBTC)