I've also got a rifle and barrel so, I've done some figuring but haven't finished it yet.
If you don't want to enlarge the bolt face, you can use 225 Win brass. It's long enough but, the necks might be a little thin after expanding them.
You also have a extractor problem, in that the 8x57 extractor is made for the case rim to slide, up into it.
I was going to try to narrow the extractor, to about 1/4" and thin next to the bolt so, it might be able to clip over the rim. I have done that yet so, I can't say it will work only that it might work.
The other option using the 225 brass is to let it feed from the magazine and modify the mag and feeding ramp to suit.
Yes, I know 225 is hard to find. I have one on a HW but, sometimes you get lucky