I'm not certain just what a "closet" sawmill is, "vest pocket" to describe something small maybe?
Not all at the same time nor specifically C&S ownership sawmills were mentioned at Morrison, Buffalo, Webster, Jefferson, Divide, Nathrop, Hancock aka sawmill curve, Pitkin, Keystone. I'm sure there are other places mentioned in other books.
I doubt you will find a quintessential Sawmill served by a spur or siding(of the Model Railroad variety) anywhere along our favourite line(s) as most were scattered off line, or adjacent to the railroad for easy loading on team tracks/public sidings. Most seems to be rough sawn if that but usually Mine timbers, Stulls and Crossties. Beaver Brook on Clear Creek, had a proper loading spur for cut Boards but these were trans-shipped from horse drawn wagons.
I do not recall exact pix. I do remember an over-track crane/rack for
loading and stacks of material waiting to be loaded. Seems to me, I
recall the material was sawn, but I could be remembering it wrong (?).
Did Klingers have a good pic in the High Line book ???