All my savages are small shank with smaller cases and I think you have to have the large shank at least for the 338 Lapua. I have not seen one built but heard that it can be done. I would start with Fred at Sharp Shooter Supply. If anyone has done it, he has. The RUM definitely is supposed to be on the large shank. the savage action might be the limiting factor here but not for sure. Fred can tell you accurately.
The 338 Lapua case will do what you want with room to spare. In fact, Tom Sarver in Ohio broke the IBS world record with shortened Lapua cases(called the Hulk), and 240 SMKs, 1.403" (5 shots at 1k) 50 score and 5x. The cases had been reloaded 54 times at the time he broke the record. He had 80+ reloadings on them last time I knew and anneals each time.
there is a thread here somewhere talking about the Hulk and the record. Of course some doubted that the Lapua can be reloaded that many times.
New World Record - 1.403" at 1K
300 Hulk- 56 firings same brass