The Satoshi is a stupid unit. Make them all nano in that range. There's no need to break up the standard greek prefixes.
I was thinking why start with 3 decimal places? Most, if not all, currencies go to the 2nd decimal place, which represents 1/100th of the whole. The idea of 1/1,000th is foreign to everyday people/cultures.
I propose the following schema, which takes care of the Satoshi breaking the pattern.
9.876543219 BTC
87 centibits
654 microbits
321 satoshibits
But that doesn't work.
If you're proposing that the 'micro' in your 'microbit' is not the standard SI micro.. then I don't think you'll get any agreement with that around here.