According to Wikipedia's summary of the situation, the French are to blame for the ambiguity - no surprises there! ;) But if we're going to avoid Americanisms, the better way is simply to use the word 'milliard', which makes perfect, unambiguous sense in any language.
Oh, good point... Right, back to the drawing board - how about "kilocount" for a thousand, "megacount" for a million, and "gigacounts" for a (short) billion? The prefixes were apparently resurrected from the Greek for use in the metric system, but haven't had any other contradictory meanings as far as I can tell. I know I'm mixing up the Greek and Latin roots with "-count", but "kiloarithmos" is two syllables too many!
Does it mean something other than 1,000,000,000?
EDIT: Apparently in some cultures, it means a million million, ie, 1,000,000,000,000, or what most people would call "trillion".
https://en.wikipedia.org/wiki/Billion