6.3 is close to 6.35 which is metric .250"

How about a case based on the 7.92 x 57R, as used in a lot of single-shot arms, doubles and Drillings, necked down? After all, there were lots of variants on the rimless version.

However to work in a Ross-length magazine and to also be rimmed, could it not be another variant of the classic .25-.303 as used extensively in Australiaicon and in different versions, in Canadaicon? A "raw" .303 case is 56.44mm; so, close enough.