There are three basic types of Schmidt-Rubin, the Model 1889 (and a slightly shorter version called the 1896), the Model 1911, and the Model 1931. The first two (or three) use the pin in the left side; the K31 uses a spring loaded ejector that comes up from the bottom of the receiver.
For the ones with the fixed ejector (which it seems is the type under discussion), if the empty case is dropping down, the fault is in the extractor. The bolts have an edge all the way around to support the case rim and the extractor should hold the case back against the bolt face until it strikes the ejector.
I don't know what parts are available, but try
www.gunpartscorp.com for an extractor. Be sure to specify the model. The 1889 has a long magazine with a lever to lower it as a "cut off". The Model 1911 has a magazine almost flush with the stock.
Jim