RT2506, I don't agree with your statement about 22" barrels not working at 1000yds. My Dad use to shoot service rifle matches with the Army Marksmanship Unit and all he shot was an M1A .308 with a 22" barrel. They shot superb groups with these rifles even with iron sights laying prone and never had problems at 600yds and even at 1000yds. He has his own personal M1A with a Springfield reciever, Hart heavy stainless barrel, tuned trigger, beautiful walnut stock, a Brookfield mount, and a Nikon Buckmaster sitting on top. The rifle is properly bedded and shoots 1/2 MOA groups. We handload all the ammunition for it using Federal Match Brass and Sierra 168gr SMKs.
Now back on topic, I would say shoot Hornady Match ammo loaded with 168gr A-MAXs like benchracer also suggested. This slug will shoot both superbly accurate and expand well on game. I advise against shooting animals with BTHP match bullets because expansion is not very predictable like RT2506 mentioned. I wouldn't recommend Nosler Ballistic Tips though, have seen them blow up on game. A better more suitable designed hunting round would be the Hornady SST, which also shoots excellent but doesn't always have the high BCs like match bullets. Hope this helps!