You are asking a lot. A bullet leaving the barrel of a 270 at over 3000 fps at 15 or 20 yards, pretty much will zip through a deer before it even knows it's there. Asking it to expand before exit is asking a bit much. The chances of even a 30-30 blowing through a deer at that range is excellent. It doesn't really matter what cartridge or what bullet is in the cartridge at such short range it's not going to be able to do much in the way of expansion. I have been shooting a variety of different cartridges, mostly those derived from the 30-06, the .243, .270. .308 as well as the 30-06. I stick to these cartridges simply because, despite the current ammo shortages they are still available pretty much everywhere due to their popularity and I have been pretty successful at reloading because components were available. Last year I was hunting with my .270 using Federal Premium 130 gr Nosler Partition ammo. I shot a buck at 110 yards and yes the bullet went in one side and came out the other. It hit the deer travelling around 2800 FPS, which is still darn fast. The bullet did do an entrance and exit the other side however the exit hole was the size of my fist. I don't have any idea how far the deer might have ran since it dropped in place and never moved, but if it had there would have been a good blood trail and probably not more than 50 to 100 yards.
Over the years; and there have been many years hunting, that a lot of hunters suffer from the, "Bigger is better," syndrome. Shooting a deer with a bullet designed for Elk, Moose or big bears is bound to result in poor expansion at any range. Tune the rifle, the cartridge as well as bullet to the game you are hunting and your success as well as bullet performance will shine.
Many years ago I was in a gun shop buying a new Winchester Model 70 in 30-06. While I was there another hunter came in and wanted to trade in his Remington 700 which coincidentally was chambered in 30-06 for a 458 Winchester Magnum. His story was that he shot at and hit a big buck and the deer ran and kept running despite being hit with the 30-06. His thoughts were that the 30-06 was not big enough for big deer and wanted something bigger that would put a big deer down. Need I say more?
Now let's talk about the big one that got away. If the bullet had hit the deer where it was supposed to, it would have penetrated the heart and lungs. No Deer, Elk, Moose or Bear is going to go very far with their heart and lungs with holes in them, which will happen regardless of the round fired if the shot is placed properly, even if the bullet does not expand at all. This is how people who insist on hunting deer with a .223 or 5.56 kill the deer. Its not due to massive shock, it's simply because the bullet destroyed the organs that keep the deer alive. Will a deer hit by a .223 drop in place, probably not. Will they run and die shortly after being hit in the bread basket? Most probably wont make it beyond 40 or 50 yards. Anyone that claims they hit the deer, or for that matter any other animal and it ran for miles simply did not hit it where it counted.
The moral of the story here is choose the rifle and the ammo to the game you are hunting and make sure you hit that animal where it counts.