Go bigger.
I've taken a dozen small to medium whitetail deer with the .22-250 at ranges to a little beyond 400 yards and, IMO, it's just not enough for humane kills and sure stops when distances exceed 200 yards.
Almost all of these deer were shot as crop damage animals in open fields, incidental to late season groundhog shooting. I've hit them with several bullet styles, from 40 grain HPs and 40 BTs to 55 BTs and 55 BTHPs. Up close = lightning. Far away = failure.
I had one animal return to feeding after a lung shot at 375 yards, and I thought I shot over him. I held lower and shot again, and that bullet landed on him near the bottom of the rib cage, and all he did was jump and look around. I thought then that both bullets must have gone under him, so I adjusted my hold up and shot one more, which spined him and he dropped on the spot. When I skinned him, I had three bullets about 4" apart in a vertical line up his rib cage. Any would have been (eventually) fatal and all passed through w/o expansion.
That was just one of several long range deer where the bullet simply didn't carry enough energy to provide the violent expansion we expect of a .22-250 and/or the impact required to get the animal's attention. Others I've shot long walked or ran away, and left no blood trail. Only because I'm persistent in following up a shot I think is good were they recovered.