Thanks to the University of Montana digitizing all of their theses, dissertations and professional papers, tonight I found the earliest reference to Better's Station that I have found. Here is what Don Bert Omundson's 1961 thesis "Study of place names in Missoula County, Montana" says about Clinton:
T12N R17V. Small community 15 miles e. of Missoula on the N.P.R.R. and C.M. & St.P. Named in November, 1889, after Henry Clinton. It is undecided whether Clinton was a railroad man or a lumberman. (Mrs. Nettle, Albert Partoll)
Previous Names: Better's [sic] Station, Pine Grove, Blossberg.
(1) Originally Better's [sic] Station on the Mullan Road, a stage station which received its name from Austin Betters, who homesteaded the townsite. Betters, the father of the informant, came to this country in 1881. The stage station was established in 1883. (Mrs. Nettle)
(2) The N.P.R.R. originally called this settlement Wallace in the 1880's, but the name was not accepted by the p.o. (Lukens)
(3) The descriptive name, Pine Grove, superceded [sic] the locally accepted Better's [sic] Station for a short time, probably two or three years. (Mrs. Nettle)
(4) Blossberg was adopted in 1888 or 1889, but was soon abandoned when it was discovered that the p.o. was being confused with another town of the same name in the vicinity of Butte. (Mrs. Nettle)Based on Omundson's claim that his thesis is one of the first comprehensive collections of origins of place names in Montana, and the fact that information that has appeared in later sources references much of the same information contained here, it's probable that this was the source material for those later sources. Also telling is the fact that Omundson, himself, had to rely on personal interviews, rather than published source material for his entry on Clinton.
I find it somewhat disconcerting that my great-grand-aunt, Fannie Nettle (Austin's daughter) was the primary source of the information about Betters' Station. I think I would have felt better if the information had come from a personal interview with someone else. Fannie would have been over 90 years old when Omundson interviewed her, and while I've heard that she was still pretty sharp in her nineties, it's plausible that she mis-remembered this fact, or got Baker's Station confused with Betters' Station. Other scenarios I can imagine: Fannie was trying to improve the Betters name by rewriting history ever-so-slightly; or Betters' Station was what the family called it, and no one else used that name.
The real gem in this source was found on the last few pages (after the bibliography, although it appears that they may have initially been at the beginning of the thesis). These pages were titled "Miscellaneous information from Missoula Courthouse records about some of the places and men mentioned in the following thesis." Here's what it said about Clinton:
Austin Betters and Charles Harris jointly bought "Pine Grove House, a restaurant and bar in Pineland Grove" on April 14, 1883. It was located "2 miles south of Wallace District on road from Missoula to Bears Mouth".
LW Frank sold the land to Betters and Harris; he was postmaster at Pineland from Oct 30, 1882 to April 2, 1883, while Edward Frank preceded him as postmaster from July 28, 1882 to Oct 30, 1882.The date and geographic location match up, but I'm not sure whether or not this provides support for the notion that a stage station was established here in 1883 and the town took the name Betters' Station for a time. However, this does give me additional things to search for ("Pine Grove House" and apparent business partner, Charles Harris).