Honestly, in my opinion, making a sidechain with the two way peg to bitcoin at 1:000 one way and 1000X the other, would do the trick.
Let's say, it would be called "coiny", "b-buck", 'bitty" or something else entirely.
you buy a cup of coffee with "coiny" on the sidechain, but you do investments, buy a car, a house, etc on the main chain (bitcoin).
Stick to metric system and just came up with a name for 1/1000, 1/100, and 1/10 etc. of BTC.
Sidechains, pegs and slang names will complicate everything even more.
well, US and UK don't use metric system in almost anything, except money.
unless you are a scientist, millimeter or centimeter tells most US inhabitants very little.
the best bitcoin people come up with is "bits", but they are currently too small, coffee would be 4000-5000 bits.