I shoot that very same rifle. Rather than re barreling it I put an H-S Precision stock with the adjustable butt and comb on it and a Nightforce 5.5X22X50 on it. The throat is so long the bullet falls out of the case on my Hornaday OAL gauge long before it hits the throat and if I want it as a repeater its going to have a huge amount of jump. But with that said I went to the Sierra MK 175 grain and just jump the bullet a bunch which that bullet will do and the gun shoots like a dream. I would like to have a break on it so I can get back on the scope and watch my hits better but most times I can past 300 yds but this is just the bad things about the gun.
Now for the good parts. I love that gun and cartridge. I never have problems finding bullets or brass or powder that it likes. I load it with reclaimed LC machine gun brass that I got for free due to what it was and even though it took a lot of work to reclaim it and get it sized it didn't cost me a thing and I now have close to 1000 rounds of really good brass after fire forming it by shooting it which that just gave me more trigger time. The gun shoots very small groups all day any day and is my confidence builder for shooting long range. When I start shooting real crappy with my big guns I just get that gun out and shoot it for a couple sessions and I am back in business shooting little groups again. It will teach you how to dope the wind and how to dial up for long range and will allow you to shoot a lot more than you can the big guns without making your shoulder sore.
I have shot it out to 1000 yards with great success and shot less than MOA groups all the way out there with it. While practicing with my .264 WM this year and getting beat up a bit I switched back to my .308 and my comment was Why am I beating myself up with the .264 WM when I can do the same thing with the .308. I ended up staying in there with the .264 WM this year and did well with it. My buddy who is just starting into long range and has a .308 in a custom rifle
took his this year while hunting with me. We spotted a really nice buck at 800 yds. He got set up and I checked the wind and ranged it and checked the drop tables and called his drops and windage and he proceeded to knock that sucker off his feet. I think that 800 might be about as far as I would try shooting a deer but I does not have a bit of a problem doing it at that range and doing it quite well. Stay with what you have and build on it. When the barrel is gone then worry about what your going to do with it.