I don't think you said weather or not you hand load. Nope, I don't see it. I've used a lot of magnums and got over them years ago. I'd choose the 7-08 and if I was reloading, the 280 Rem. The beauty of the magnums is they deliever massive power at normal range. But more and more we see them used to justify shooting at extream range. But out to a couple hundred yards, the 7-08 or better the 280 Rem is more then enought. The advantage of the 7mm's over the 270 is their 160 and 175 gr bullets.
Then, if the opertunity to hunt moose comes along, you've an excuse to buy yet another rifle if you want. Personally I don't have a problem with either of the 7mm's on moose either. They've got the bullet's to do the job and it's about bullet's. Of course if your thinking of shooting moose at 300+ yds, I think I'd opt for the 300 mag with 200 gr bullets. Actually if I were shooting at a moose, I'd just get closer. I've used the 7x57 a great deal and my guess is the 7-08 is about on par. I've also used the 280 a good deal and would never choose a 7mm mag over it and I've used the 7mm mag a great deat also.
If you wanted a 30 cal, I'd stick with the 30-06, and I'm not a 30-06 fan, but I don't like recoil much either. I've worked with some 300 mags and owned a couple 338 mag's, that is past tense.