New printed money preferentially attaches to existing money 
Nope. Read the article you linked. Cantillon effect is about path dependence as money enters into circulation. It would apply even if, for instance, a communist revolution used a jubilee and UBI to inject money very differently from current distribution.
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My claim is that new money mirrors old, *whatever* the distribution. It’s a complementary claim that can be true even if the cantillon effect happens to not hold.
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