The twist rate on the .270 WIN in the Tikka's is 1:10"...so bullet weight shouldn't be the problem here. As Sheridan mentions though, I would also recommend continuing to try different loads and bullet weights. My Tikka in 270 WSM shoots real well, but I had a couple early loads it did not like. My .270 WIN is an older Remmy 700 BDL and I provided the load I have had the best luck in it, which produces MOA groups.
One thing to consider...not picking on you, but just putting it out there. Just because you can produce good groups @ 100 doesn't mean you'll be able to duplicate that performance out to 300 with a new gun immediately. It takes time with a new rifle to develop accuracy the further out you shoot, even with a leadsled. It may also just need some good ole break in time. Not every rifle shoots like a dream out of the box, may take 100 rounds or more to get there. Did you follow one of the well recommended barrel break in procedures?