Rost495: Take it from someone who has done it - use your 22-250 with good 55 grain bullets, patience and good shot placement and put a "big hole" right through the heart/lung area of Deer and Antelope.
Then go collect your trophy as it will most often be dead right there and NO meat wasted.
Unless you eat the heart or lungs.
No mess, no muss, no fuss - that Deer/Antelope will be WELL bled out and your "meat" will not be wasted at all.
Hold into the wind
VarmintGuy