Hi shamus, at first I recommend you first read Jon Speed's books "Mauser- Original Oberndorf Sporting Rifles" and "The Mauser Archive"! You are right, 6097 is the Mauser commercial number. Speed's book date this number to 1902-3. No, Rigby never made any actions. The conventional thinking is: Rigby bought the actions from Mauser and barreled and stocked them. According to Speed's researches, it was not so. In his "Archive" he shows a photo from the Mauser factory showing barreled actions, complete with sight bases, they made for Rigby. All the pre-WW2 Rigbys also show German proofmarks, so the barreled actions were at least "in the white" when they left Oberndorf. And Jon told me once he found an entry in a 1920s Mauser factory inventory that translates to "stocks for Rigby rifles". So, even if this upsets all fans of the "British Rigbys",apparently Rigby did very little in making the Rigby bolt actions, but bought them in almost completed from Mauser.
6009 is much to low for a Mauser .416 serial number. Speed lists .416 Rigby # 5704 which was built on Mauser # 97228, dateable to 1928-29. As I wrote, you will find the Mauser serial number not on the outside, but under the receiver ring and on the rear magazine wall!