Ideal solution to my taste is a revamped combat system to one like in Salem - where skills are time and skill based. I.e. hunting Aggropelters is also a lot of running around, but this running is fun compared to chasing fleeing animal. The card-game combat is interesting in terms of game-design, but IMO it doesn't fit really well such type of game. You just stand still and play cards with bears and bulls - it would be much more fun to evade aurochs rushed run towards you, and time your attack to hit it in the process!
But since this is not happening, here are some other thoughts:
- People cheese animals because they flee - make fleeing threshold further away (i.e. half-dead animals don't run away, only 90% dead animals run away - basically when the fight is already lost). Make their run away speed slower compared to healthy animal.
- People cheese animals because animals are stronger - via using boats or entering caves or houses to close openings. Make animals deaggro targets that can't be reached much faster, so you can't really do much without facing the beast again. So you will have to have needed stats to fight, and not cheese. There are some possible exploits to this, though.
- People are cheesing animals using alts - don't have much to say about this, I hate alts (and botting), so my suggestion is to ban alts

Also, additional mechanics to hunting would spark it up. Fights are different only for which cards do you use - I don't have much experience with hunting - but since it's a deck-building mechanic, there is probably the most efficient decks, that make the fight basically the same all the time. I like how trolls can cause cave-ins, so similar interactions with more animals would be really fun IMO.