Factory load particularly for a 26” .223 Shilen bull barrel, 7 twist?

No one has shot your barrel so they can’t tell you what works for it. You can have two of the exact same barrel and they may like different things. It’s a 7 twist .223 so will shoot the heavy bullets for long range so just buy some and try it. For shorter range anything will work as far as weight.

How far you plan to shoot it?
 
No one has shot your barrel so they can’t tell you what works for it. You can have two of the exact same barrel and they may like different things. It’s a 7 twist .223 so will shoot the heavy bullets for long range so just buy some and try it. For shorter range anything will work as far as weight.

How far you plan to shoot it?
500 yards. Shooting at 3 and 4” gongs.