If I understand your question right you seem to have the code that seems close to what you want, but doesn’t function correctly. What I have trouble following is that your description talks about taxonomy archives, but your code seems to be about custom post type archives.
I would suggest to use more appropriate query methods rather than working with vars directly:
$query->is_tax()to check for taxonomy archives$query->is_post_type_archive()to check for CPT archives$query->set()to modify query vars