Some times you got to pull up your skinny jeans, slick your manbun back and grab one of those big, mean, and loud guns to get the job done. All while not spilling your vegan latte.
I am in the 300WSM club and shoot 190 CX out of mine. For the yardage you are looking a 308 would work with a 22" barrel. I prefer short action rounds personally.
I am loading 155 Lapua Scenar's in my 20" .308 and have had great accuracy and they worked well on game. I am loading with F210 and Varget for around 2875 if this helps. I too normally go mid to heavy but they have great BC for weight and are accurate.