The belt of a 7mm Magnum could easily be turned down to the proper size for the base, at about .525"(13.35mm). The rim is only .532"(13.51mm), but would still likely work if in good shape.
The case, trimmed to length and sized, and perhaps inside reamed or outside turned, whatever is necessary.
As well, a larger rim (.573" ring) can be installed and sweated on(soldered) for BP loads.