I have used the 22-250 for deer (and should I even say this since I'm a magnum user[&:][&:])and have shot a few elk with them(cows).

I used the 55 TBBC on all 5 ocasions and hadone follow up shots on the elk.
On the deer the TBBC penetrated right behind the shoulder and was lodged under the hide on the far side.As for the elk The first elk I killed with one I was 16 years old and it was the only gun in the truck.I put one right behind the(Right) shoulder and it penetrated through the lung and stoped inside the other,I had to shoot her in the neck to put her down.The second elk she was so close I shot her in the head at about 20 yds and she died right on the spot.
I don't advocate .22 cal's for hunting and they should only be used with extream prejedus(sp).But I have seen them work on deer(white-tails and mulies).
Best of luck with your .22-250 they are great kids guns and sounds like you have a walking varmiter on your hands also.
BBJ