I've come up with a system I think would work best, I think grouping animals and calibers into classes should be scrapped completely.
Instead of them, I think it would be best if each caliber had a list of species ethical for them, it would be long of course, so maybe you could filter animals in the list by map to shorten the list, or add a simple search bar to search a species you want to check for if it's on the list. And also vice-versa, searching an animal in the codex shows you a list of calibers ethical for that animal.
This would solve problems such as for example using a .30-06 in plains bison but not water buffalo, or using the .30-30 for black bear but not elk.
Having no set classes means animals are more fluid amongst the calibers.
Of course this change would be a lot of work with deciding calibers ethical for each of the 106 species and pairing them with specific calibers out of the 50-ish we have in the game already, but I think the work would be worth it in the long run in creating a better experience overall.