The freebore diameter on your Shllen barrel is very close to bullet diameter. If you were to look at the reamer print the freebore dimension would probably read something like .2643 to .2645. When you only have a few "tenths of space on each side of the bullet even a full 001" can be a big deal. The fact your .260 factory ammo with smaller bullet diameter isn't having the problem should be your indicator. Factory chambers can be one or two thousandths larger than the bullet but that doesn't do much for accuracy.

Your bullets are nice and snug in the freebore and should shoot just fine. In fact they might shoot better than the smaller diameter bullets.

FWIW, where are you measuring the runout when using the Hornady gauge? At the neck? Bullet bearing surface? Shoulder? I prefer to use a run out gauge that supports the case just above the head and again at the shoulder. This tells me how the bullet is meeting the freebore.