Research completed.
The 300BS does use the 307Win or 356Win parent case. It can also use 444Marlin with some extra tweakin'. Standard 300 Savage dies, and load data from the 300 Savage is where things start. The 300 Savage cases cannot be fired in the 300BS chamber though, as the chamber is cut deeper to prevent that. Data I have shows a 150gr @ 2400fs. If memory serves the 309JDJ runs the 165gr @ 2400fps. So the 300BS falls right in between the 30-30AI and the 309JDJ. For what it's worth, most recommend just going to the 309JDJ. If you don't mind the price of the barrel the custom dies don't matter either. If you're trying to stay on the inexpensive side. The 308Bellm or 300BS will work well.