shouldn't cause problems, according to some sources
This stuff (8x57 JR) was supposed to be loaded to essentially the same specs as standard rimless 8x57 J/JS, just built with a rim to facilitate use in single-shot sporting rifles primarily built and sold in Europe (according to Lyman's 48th). I can see no appreciable reason not to do what you've proposed (transferring components to rimless 8x57 brass).
"A lot of people go through life doing things badly. Racing is important to men who do it well. When you're racing, it's LIFE. Anything that happens before or after is just waiting."
-Steve McQueen, 1970
The Second Amendment: Established 1789-1790; Under Seige since 1934