LS, since this is a tacky rifle, depends on how much time you expect to spend 600yds and out. The further you want this rifle to smack, the larger the case and bore.
I also assume that you want a mag fed platform that can handle field use. Something that doesn't weigh a ton or super big/long. 24" pipe as a nice compromise. gives you a chance to mount a brake or 'can' without feeling like you are shooting a musket.
If so, I would eliminate all the improved cases/wildcats and go no smaller then a 308 case volume.
If willing to only use center feed mags, sharp shouldered cases will feed but in a staggered mag, you will eventually have hang ups. So the AI or Savage mags would be needed.
In the 6mm, I would look at a 243 with a 7 twist (maybe even faster) and push the 115gr+ bullets as fast as she will go. The 243 improves are also very nice but there is that mag restriction.
In the 6.5, 260R is the base. If willing to use Center feed mags, the 6.5 Mystic/260AI are very nice. If only going with a 24" barrel, the 6.5-284 would be my choice for an effective 1000m rig. I would build it on a Savage short action and seat the bullets to around 3.0".
In a 7mm, the 284 is just about big enough for 24" pipes. I would prefer the 280 and 7Mystic/280AI as a min. This may surprise you but I think the best in the 7mm for a working rifle would be a 7RM and 162gr Amax or 180gr Bergers.
I have skipped the WSM as I have no first hand experience and they usually don't come in dmags. Also, seating a 180gr Berger to fit in a short mag would limit case volume. Wouldn't use it in a long mag.
The small cases now popular in BR work because you can put them in zero tolerance actions with very long barrels. That allows you to run very high pressures without problems. This is not something that a working rifle will allow and having to hammer a bolt open during field work is not condusive to fast follow up shots.
At least, not from you...
Jerry