I'll agree it is probably the bullet, but not because it won't stablize in your rifle. The Remington 100 grain core lokt bullet isn't any longer than the average cup and core 100 grain bullet. I bought a bunch of 150 grain core lokt bullets to shoot in my .300 Savage rifle. Couldn't get anything to group better than 3". After I went throught the normal things like checking the scope and mounts out, I tried some Sierra's in 150 grain and printed several groups less than 1.5 and a few less than 1".
So the only thing I did different was change the bullet, used the same powder, primer, case, and seated to the same lenght. So on further investigation I weighted the bullets, there is a huge variation in bullet weight and these were all from the same lot. My bullets weighted anywhere from 147-152 grains, so I seperated them by .5 grain graduations. Loaded a few up and shot them POI would shift but they grouped pretty much around 1-1.5". The Core Lokt isn't a bullet I'll be buying for reloading again.
I had a buddy who rebarreled his sons .243 Win and bought the Core Lokt bullets to reload to break in the barrel. Had the same problem, nothing would group better than an 1" on a blue printed action with custom barrel. I told him to weight his bullets and he found a pretty wide variation in weights as well. It wasn't as large as mine, but when he sorted by weight the grouped okay as well, nothing spectacular but well enough he wasn't thinking of taking the rifle back to the smith.
I don't normally weigh bullets ever, but because of this problem I've weighed a few hundred Sierra, Nosler, and Hornady bullets. I've never found them to have more than one grain difference usually around .5 grains from what they are supposed to weigh in a box of 100 bullets. I don't know who makes the Core Lokt bullet for Remington but they don't have the same standard of QC other bullet makers have.