If your 223 has a 1:8 or 1:7.7 twist, try that at 600 yards. I have been shooting XTC and Long Range for several decades, mid Range has popped up in the last couple of years. Ballistically the 80 grain SMK or the 77 SMK is similar to the 168 SMK at 600 yards.
A bud of mine has been shooting his 223 scoped AR at 600 yards and I copied his idea with my match AR. I am a sling shooter, shoot prone with a sling. I was very happy with my 223 at 600 yards. With that 223 I don't break position and it does not knock me out of position. That makes a heck of a difference on paper and anyone who has been a competitive shooter knows the importance of a consistent position. I was loaded and ready to fire once the target came up, I only shot when wind conditions seemed predictable and consistent. If the wind picked up a little bit I shot on the edge of the ring and adjusted my aimpoint by my impact. If the wind really picked up, I stopped and waited for it to subside. I recall shooting HM scores and the high X count really perked me up as I have been struggling with my scoped 308 at 600 yards. It is too heavy and knocks me out of position each shot. Incidentally I shot my 75 Hornady’s at 600 yards and they hammer just as well as the 80 SMK’s.
If you really want to use a 30 caliber, try the 308 Win. The current “hot” target load is a 185 Berger, 44 grs Varget, Laupa small primer brass. This may be so hot that you blow primers in your gun so work your way up. I have been told the best barrel/twist combination is a Krieger four groove 1:12 twist. This is from shooters on the US F Class tactical team, and this is their 1000 yard load.
For 600 yards, a 168 Match, better yet, the 175 SMK, and I have shot thousands of 190’s.
Any of the 6.5's will be a great choice, just that they eat barrels faster than a 308. Until such time as you are shooting consistent Master scores, don't sweat the difference between 223/6.5/308. The greatest difference on paper will be due to you.