Any modern centerfire .243 or larger should get you that far with ease, and there are a number of new inexpensive rifles that have a good reputation for accuracy out of the box, (Ruger American, Savage Axis, etc)
.223 can do it, but you need a fast twist barrel, faster than what tends to come on bolt actions (other than "tactical" ones.)
You may also be still able to do it with your Mauser, have you tried anything to improve the accuracy? There are some instructions here for a K98, most of it would probably apply to yours.
http://www.mausershooters.org/k98k/SC_tips2.html