Hmmm .... We had the 3' Spokane & Coeur d'Alene that ran from Cataldo, Idaho to Wallace as part of a 3-tier transit system - standard gauge to the wharf at Coeur d'Alene, steamboat down the lake to Harrison, then up the Coeur d'Alene River to Cataldo, where the 3' RR ran the last leg to the mine area.
As Whitman County is the next county south of Spokane County, and the UP accessed the Silver Valley from the south, perhaps this is somehow related ?
Steamboats plied a number of our larger lakes in those days, but the dual gauge is baffling me. Whitman County borders the north shore of the Snake River, another steamboat thoroughfare, but I am unfamiliar with any NG there. The NP built trackage into Lewiston around 1905, but that was standard gauge and I am unaware of any NG interchange along the route.
Another option would be the portage RR's that operated around the falls up and down the Columbia River. There were several. I am unfamiliar with gauges on these though.