Heavybarrel, exactly how are you "cleaning" this barrel???? When you believe you have it clean are you able to look in the bore with a borescope??? I am going to guess not.
Remington barrels typically have some tooling marks and they also typically will copper up, especially when new. I can tell you that for certain, many people claim to have "cleaned" their rifle and many honestly believe the bore is clean and that the product they are using works great...when in fact it does not.
I have tried them all and found only a few bore cleaners that really work and get the copper out. Some very popular ones will work...if you leave them soaking in the bore for a week. Your rifle sounds exactly like a typical copper fouled bore that is not getting really clean.
At this point I would suggest your next move to be to find someone with a borescope and have it looked at BEFORE you spend any more money or try any other "remedies". Maybe it's not copper fouled and maybe you are truly getting it clean, but I can tell you I have seen scopes replaced, barrels replaced, stocks bedded 3 times, triggers bought, bullets and powder changed and tried, rests, benches, shooters, targets, and the only thing wrong with the rifle was copper in the bore, an owner not willing to believe it and bore cleaner that does not work.
Personally, I have had very good luck with Speer TNT bullets. I have a 7mm-08 that will put them in the same hole, but it wont do that with Match bullets.