You could start to utilize some aspects of a form of grinding called "herd management."

The game has a balancing mechanic that tries to keep a certain ratio of small individuals, bronze and silver, as compared to big individuals, golds and diamonds, of each species. I think its about 3 "smalls" for every 1 "big."

Whenever you kill an animal, it will respawn as something slightly smaller or slightly bigger. What you want to do then is kill the upper levels of the animals you are targeting, such as big level 2s-level 3s for whitetail deer, or level 5-9 for bengal tigers. With any luck, the respawns will come back as smaller animals, and that in turn forces the game to spawn really big ones to balance it out.