FIRST OFF: a little lesson about hunting rifles vs. target rifles--->1MOA at 500yrds doesn't really depend on the cartridge, it mostly depends on the shooter, followed by the rifle. Expecting 1MOA accuracy from a hunting rifle at 100yrds is usually a stretch, maybe not a big one, but typically 1.5MOA is what you'd be glad to get...at 500yrds, 2MOA is very good for a hunting rifle. The Encore is incredibly accurate for what it is, however, it's not likely that you'll get 1MOA at 500yrds with ANY round out of it, you might, but it's not likely.

Your post seems as if you're as new to hunting as you are to hunting rifles, so I'll give this advice: making 1000yrd shots on paper is one thing, that's with target rifles and match ammo at a known range on an inanimate target, known wind, and typically great shooting position (if not from a bench)....Hunting couldn't be any different than that if you tried to make it so. 500yrd shots on game are just unnecessary, maybe you can make them ethically, but there's no sport in it, getting close to game is what's sporting.

Having a target rifle in a cartridge doesn't mean you have a hunting rifle in that cartridge, if you already reload for .308, I'd suggest you get a .308. If you really want to buy a different cartridge, I'd buy a .30-06 or .270, great hunting rounds and incredibly versatile. The .25-06 is also the same case as the .30-06 and .270, but its light weight kind of limits its uses, for TX it'd be great, but if you get a chance on huge hogs or travel to find bear, it's kind of light.

The 7mm-08 is a great round, which would be a good use of your mis-weighted .308 brass, it's probably a little lighter recoiling than the .25-06, never shot them close enough together to really decide, but they're both pop guns.

The .243win is also a very versatile cartridge, easily handles deer sized game, however it's not too over powered to be used on jack rabbits or coyotes (probably the perfect coyote rifle).