.44 Alpen
This discussion reminds me of an article I clipped from a back issue of "The American Rifleman", dated some time in the late 60's, early 1970's.
The author, Roy Chandler, built up a custom Mauser bolt rifle on a .44 cal wildcat he named the .44 Alpen. Chandler took a .300 H&H case, cut it off at the shoulder, and ran the case into a .44 mag sizer, which allowed the 240 gr slugs of the day to seat nicely. He had the barrel twisted 1-20. The rifle would get 2500 fps+ with the 240's. Interestingly, he laments the lack of factory jacketed bullets above the 240 weight, which sort of dates the article.
Chandler claims he used the H&H case because it solved headspace problems using other, rimless cases. I suspect it also simplified the problem of the rim on the .444 Marlin, which was on the scene, (he references it in the article), but it seems he elected to go with the wildcat Alpen anyhow.