believe it or not, the very first 8x57 was the 8x57IR with a mauser A-base rim. the german military try to rebarrel and rework the Mauser 71/84 before they switch over to the M88.

I would not recommend to rebarrel the 71/84 into a rimmend 8mm. there must have been reasons the german military dont go this way. but there is a very easy possibility: the Steyr made Kropatschek M 1886 in 8x60R

the original blackpowder loaded 8x60R was successful changed into the nitro loaded 8x58R ,iirc, in the 1890s.
you can see that the Kropatschek based on the Mauser 71/84.