I am no expert on Sapir-Whorf lore. But I understand it usually concerns itself with semantics and the lexicon.
Would it be possible, do you think, to look at languages with similar and different clusters of parameter settings across the world and devise experimental studies to see if syntactic parameters affect the way we organise the world in our minds?
This might provide opportunities for interesting debate between proponents of Chomskyan and other types of modern linguistics. Of course, someone may already have suggested such an idea, in which case, feel free to admonish my ignorance.