I have done exactly this with a Lithgow No.1 Mk.III*. Many years ago, a gunsmith friend of mine moved into town from his rural block, and had to 'rationalise' his stock. He had a .375 barrel blank left over from the buffalo days, which would now never be used on account of the influx of cheap BRNO .375 rifles at that time. We built a .375 JDJ facsimile because the JDJ reamers are proprietry (patented or somethin', so the story goes), and only JD Jones can order them. We cut my chamber using a .308 reamer with a .375 throater attached, and simply pushed it in an extra 1/4-inch or so. The rim recess was then cut on the lathe.

The sizing die was made by softening a Lee RGB .308 die and shoving a 25/64 drill-bit (from memory) through it, then polishing. Didn't bother to re-harden. Works a treat.

This rifle was mentioned in an earlier thread on NE.com, I'll see if I can find it. Meanwhile, some pix (apologies for the blonde stock, the Slee XXX 'Classic' I had put aside was needed elsewhere, and I never got round to blueing the barrel either!):