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.

Except that it's a terrible word because milli means thousand, and ard just means a grammatical modification.

So all that accomplishes is conflating thousand with million with billion. (Of course "million" is already a conflation of "thousand"!)

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!