223 bolt action with 7 twist

The NOE 60 grain gas check is an excellent bullet.   Anything from 1 in 14" or faster will stabilize it.  Don't worry that your 1 in 7" twist is faster than needed.  They shoot great in my 1 in 8 or 9 rifles. See my article in Fouling Shot #261 on shooting them in two rifles with good results.  I think you will have better luck with alloys softer than linotype, unless you are going for high velocity. If the nose is the right size for your bore they will shoot.

John

Correction:  I have edited the above. I was thinking of the similar NOE 72 grain bullet when I said I had shot it in completion.  Also when I said it takes a 1 in 10" twist or faster to stabilize.  The NOE 60 will stabilize in the common 1 in 14: twist.  My testing for the article mentioned above used a load of 5.0 grains of TiteGroup which produced 1,560 fps.  The averages of 5 - five shot groups for gas checked bullets were 1.4 moa for the 1 in 14" twist and 0.98 moa for the 1 in 8: twist. I don't think that means that the faster twist is better, but it does show that what some would call an "over stabilized" bullet does just fine.