Are there any differences in meaning/usage between when NAmE Speakers saying or replying with " I would say ( that ) ... " vs " I think ( that ) ... " ?
Not much difference. "I would say that" perhaps suggests a more considered opinion than "I think that" at least for some speakers. But it could be mere style or habit of expression. "I would say" is slightly more formal. But either could be used in place of the other, and context might alter these shades of meaning.