Since I've been researching the material behind the 1896 expedition I've discovered the real possibility and most likely probability the photos published with the 1898 report were not taken on the expedition but were taken by other photographers around that time, likely 1894-1898.
Since then I've been researching photographers who were working in and around Mount Rainier before 1900, before it became a National Park in 1899, and so far I have found the following ones.
The photos in the 1898 report were attributed to Bailey Willis, the USGS and lead geologist for the expedition. In addition the USGS archives has 40-50 negatives of Mt. Rainier contributed to Bailey Willis.
Researching photographers working in and around Mt. Rainier 1894-98, some of the images in the report at identical to those taken by Alvin Waite who lived and worked around Tacoma, WA during the period. It's not clear how the USGS obtained copies of the photos and permission to use them since it would have required duplicates of the 4x5 negatives.
I have found references to Cyrus A. Mosier, appointed Public Lands Director for Washington in 1989, serving intermittent periods until he retired in 1900. The references cite a report on the forests of Mt. Rainier along with 100 of the 200 phootographs he took around Mt. Rainier in the early 1890's. To date I haven't found any references to this report or archives of his photographs.
In addition Henry Sarvant worked in the area for a brief period on this adventures around the world.
Some photographers with studios in Seattle occasionally worked around Mt. Rainier. George H. Braas of Boyd and Braas photographed visitors and climbers in Mt. Rainier, Mountaineers Collection.
Some of George Braas' photo were incorporated into an article by Isreal C. Russell, "Impressions of Mt. Rainier", published in Scribner's Magazine, Volume 22, page 169-176, 1897.
Just outside that period, Arthur Churchill photographed an 1888 summit expedition.
After that period Albert Barnes worked in and around Mt. Rainier NP, 1905-10.
I haven't fully explored the photographers from that period, lots of work left, and I haven't checked out the NPS archives yet. So, this post will be updated as I find more collections.
Blog updated 3/18/09, 11/4/09 and 8/21/12