> What if we tried to create, say, a language with a logographic written system that is pure WYSIWYM (as opposed to “what you see is how you pronounce”) and synthetic to boot?
UNLWS.
> Make it use vocal cords differently.
Dritok. Or, if you just mean "differently from Europe", any conlang which makes use of creaky voice.
> Instead of borrowing around, use a random seed in generating a minimum set of unique basic “native” words according to language rules and build on top of that (borrowing for meanings outside of that set).
So freaking common I can't even begin to list a representative set. The whole category of oligosynthetic languages does this (although the initial generation may not be completely random). There are multiple software packages for assisting with the generation of this kind of language.