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I would definitely try the stock barrel before deciding on a barrel change. The 7mm-08 in a 22+ inch barrel combined with appropriate ammunition is adequately powerful to take deer sized game in excess of 500 yards given precise bullet placement. Your rifle should be capable of producing sub MOA accuracy out of the box with several long range factory ammunition choices and any number of hand loaded component combinations.
Without getting into the ethics of your proposition, yes you could use the rifle in factory configuration to take game at 500 yds.
That said, I would expect a long range hunter to be highly familiar with all of the variables affecting the decision to pull the trigger and your question implies that you will need to do a lot more research and practice before sending that bullet on its way.
