I have a 24 in. Encore 30/06 barrel and the powder I've had excellent success with using 165 to 168 gr. bullets is Varget. It will shoot 3 shot groups of less than 1 inch to perhaps 1.5 inches with a variety of bullets including Nosler and Sierra match bullets and Barnes TSX and banded solids.
I doubt very much that you have a scope problem. First of all, try a bullet that you know has potential for excellent accuracy like the Sierra match bullet you're already using. Use that bullet to see what your rifle will do. I generally start with a Berger, Nosler or Sierra match bullet. Once you have found your load, you can experiment with other bullets. If you can't get it to shoot one of these match bullets well, it probably won't shoot anything else well. I don't think any of the bullets mentioned have better accuracy potential than the Sierra bullets you're using.
I would also suspect you have a mild load. The fact that your groups at 50 yards are good and and 100 yards are poor out of proportion to the range, tells me that your velocity is probably a bit too low. As a general rule, I've found that my Encores in various calibers shoot best at loads ranging from 75% of maximum to 100% of the maximum recommended loads. The usual precaution of working up in small increments of powder (in my 30/06 I work up in 1 grain increments until approaching maximum loads and then in 0.5 grain increments) applies.
The twist in all .308 caliber T/C barrels is 1:10.