(click on the pictures for larger views)
I've preserved a reference to the modern day Google Street View of the building for browsing the property.
A close-up look of the fence line shows the the gate between the marble property and neighboring Schutte Lumber where the rail spur ran.
A check of the city property data shows the relationship of the the right-of-way to the surrounding properties.
The exercise remaining for this modeler is to determine the era-appropriateness of rail service to an industry like this. I'm sure cut stone had its heyday when there was no competition from a highway system and trucks. The quarrying side of this industry is covered quite well in Industries Along the Tracks Vol. 4 by Jeff Wilson and that publication has a few pictures from the late 1970s of raw cut stone block loaded into gondola cars. Finishing, including further cutting would likely take place at a local retailer or wholesaler like Carthage Marble.
Rail shipments of this commodity have likely dwindled to near zero in recent years. One source I found was a mid-to-late-90s NAFTA freight study that looked at commodity flows through the greater Kansas City area. That report makes mention of cut stone products being exported to Mexico, but indicates that the shipments were handled by truck.