No Sir; your kill club does NOT represent humanity as a whole, and that is an absolute certainty.
It seems to me your "Kill Club" is approaching their goal in a bass-ackward fashion. The "logical first step at understanding their intelligence, eating habits, vision, hearing and sense of smell" should come BEFORE killing one. In doing that, and first "understanding their intelligence", it just might be that you really don't care to kill one after all. And that's a good thing. (Deliberately killing one might very well put you and your members in the history books, but overall, you would not like the kind of attention you and the group would receive from "humanity as a whole".)
Can't figure out how you could learn much about their "their intelligence, eating habits, vision, hearing and sense of smell" from the body of one.
Yes, there are many people who do know the range and population density in various specific areas of this country. It is well known to these folks that those BF that are part of family groups in the south/southeast have specific foraging areas for the seasons but their typical overall home range remains the same. They don't migrate, they just claim a lot of land.
I personally have never considered killing one. Have known a lot of people who claimed they would if they ever saw one. About ten or so of those folks later saw one or more. One man saw three walking across an open pasture less than one hundred yards from his deer stand. Like the rest of those ten or so, he never fired a shot. After looking at them through his rifle scope, he forgot about shooting one. Hopefully you will react the same way if you get in that situation.