What is the intended purpose of these rifle to hunt with, or just use the range? If the rifles are just to shoot I did find some pleasurable cartridges the play with. One that comes to mind is the 7-30 Waters, I would find an old Savage 340 in .30-30 and rebarrel it.
With your 7X57 and .270 I see no need for a 7mm RM or .280/.280 AI. If you want a bigger rifle and since you like M700 try and locate a 700 Classic in .300 H&H or 8X57. Another two interesting cartridges to me are the .358 Win and 9.3X62 and if I could find one reasonable a .45-70 built on a Siamese bolt action rifle.