There are many options including using a heavier, tougher bullet. Or a lighter tougher bullet. Either approach works, but the lighter tougher bullet gives you more options. This is the 21st century, you don't have to still use 1800's science and technology unless you just want to.
I'm loading 130 gr Barnes TTSX bullets at 3050 fps in my 308. They will retain 99-100% of their weight on impact and equal or beat the penetation of heavier 180 gr bullets. They will shoot laser flat and have less recoil. They are not the best choice for long range shooting, but perfect for your uses. I'd use 110 gr bullets in the 270.
Conventional bullets lose 30-80% of their weight on impact. That means a 180 gr bullet will only weigh 50-130 gr after impact, about the same as the TTSX finishes with.