Try the Remington Core-lokts first since you already have them.
They shot pretty well from my Handi .243 and from what I read, it's a caliber that many consider the most finicky.
I didn't polish the bore since I was getting what I consider decent accuracy for me anyway!
Don't have experience with the 308, but Handi's seem to like those core-lokts, so I would try them, and then give the Federal Fusion a try!
I tried them because of all the positive reviews that ammunition received, and found that they did shoot the most consistent groups.
I shot about 5 different brands, and I could have saved some money had I stayed with the Fussion!