Look at the Gamo Magnum at Cabela's advertized 1300 FPS, my calculator says figuring 1150 FPS with a 20 grn pellet and you have 55+ FPE. It comes with a scope. $299 and change. Maybe a Black Friday or Cyber Monday deal to be had? I have no idea about the longevity of the rifle, most pellet rifles are very accurate.
I have no idea how much use yours would see, mine is occasional use. I've been looking for something powerful enough to take out a Nutria. The one I have now is a used top of the line air rifle, Feinwerkbau, accurate as heck, not really powerful enough for anything larger than a Rat IMO. Mine will put a pointed 8grn pellet through a half-inch of Pine at twenty yards. I always prefer a quick death, I hate to see an animal suffer.
The base of the skull is almost always a quick death. I've had some iffy results shooting downwards at the eye or ear.