I have a Sauer drilling that looks identical, chambers are 65MM and the 8x57IR rifle barrel is .318" diameter. I have only shot it a little so far, but I had no trouble ordering a case of Kent Gamebore traditional 2.5" shotshells for it at my local shop. Any shop stocking Kent shells should also be able to order the Gamebore. One note about those shells, the British "#6" is closer to a North American #7 in size, and Gamebore do not offer a larger size shot. I have a current German hunting catalogue that I picked up there in January, it lists several 65mm/2.5" 16 ga. shells by Sellier & Bellot that a good gunshop may be able to special order for you from S&B. I know for sure that S&B still load the 8x57IR ammo.
I handload larger size lead and bismuth shot for my short chambered 16's, it's not too much trouble and is a fun project besides. Will Bilozir has components from Ballistic Products.
I would love to find some original Brenneke slugs in 16 ga, 2.5", but they seem unavailable. I was able to find some paper hulled "no name" shells in 16 ga. 65MM loaded with #0 buck at the Saskatoon gun show a couple years ago, so it seems that visiting the shows might be a good idea for locating odd shells for rare drillings.