I too agree with the proper shot placement. However, once you start getting out to 300 yds the Foot pounds of energy play a major factor in the damage that small bullet does. At 300 yds the 55 gr has only 603 ft lbs. Not very much???? To hit one in the shoulder, I dont believe would even begin to penetrate. Not on a large whitetail. I have shot 2 with mine. Both in the head and neck region. Fell right where they stood!!! No finishing shot required. Both were at 286 and 313 yds, with a bench rest and years of gound hog, crow, and coyote shooting experience. If you can shoot dogs, crows and woodchucks out to 400 yds then you should be able to hit a deer in the vitals or head and neck. I prefer head or neck. If you miss, no harm done. They'll be back for another day. If you are off at all left or right on a vitals shot, what happens???? Front leg or ponch and lost forever to the dogs and crows! That's not ethical to me. With a larger caliber, recovery chances are fair to moderate. The 22-250 is just too small with a bad shot.
If you want to stay with the smaller bullets, try a 6mm, 243, or 25-06. Great guns, fast, hard hitting, and much larger lead for the pencil! I have shot 3 deer with my Rem 6mm in the 80 and 100gr. Does a great job! Mine is extremely accurate. My cousin uses a 243 with an 80gr sometimes. Very good as well. Again though, both are very effective with proper shot placement.
Good luck!