There is no inherent accuracy difference between belted and non belted cases. I personally don't like belted cases because the belts severe no purpose at all and only take up case room. I also believe you will find more casehead separation issues them too.
That said, smaller cartridges are least affected by barrel harmonics and are inherently more accurate than the magnums. I.e., the 6mmBR. My smith is a competitive shooter and competes at all ranges. He shoots his own modified 7x57 and does quite well with it. He also told me, that the 2 most common winning cartridges that he sees are the 6.5x47 and 260 Rem and these are at 1K and 1K plus events.
I just had a 6.5 WSM done which is a little less capacity than the 7 RM. It's going to be about as hard on barrels as a 300 RUM. I am contemplating a 6.5/Dakota build sometime in the future. Not sure if I'm going to go with the 7mm or the 300 which is slightly larger.
The fatter straight wall cases seem to be a little more efficient than the narrower cases. The short mags, Dakotas, and RUMS are designed off the 404 Jeffry which IMO, is much better design than the 375 H&H, the grandaddy of the belted mags.
If you really like the belted 7 and want to AI it for a little more capacity, try just necking down the 300 WM which is it's slightly longer big brother. Push the shoulder down instead of blowing it up and you will have a longer neck and almost no need for fire forming. You will want to ream out the neck though to remove any donut that might form.
