Bob,
The years that you are looking for, are covered with the state censuses. My
records show a state census for the years (this may not be complete, but close):
1871;1878; 1879;1883;1885; 1887;1889; 1892. This could cover quite a few locations
for you, with the addition of the Federal census of 1900. I am not sure if these
are available through FHC. If not they are available at our local library (Olympia
WA). We do have a researcher in our genealogical society that will do research.
This could really track down all of the locations since your grandmother moved
quite a bit.
Did you contact the Sisters of Providence in Washington state? They were the first
order that came to the territory back in the 1850's (?).
My German ancestors came to the port of New Orleans & then took a river boat to
Quincy, IL & settled there. There was probably a railroad during the time frame
that you are talking about to connect Chicago with all of the locations that you
are referring to. Also Highway 90 connects Chicago to Seattle, even during those
years. My grandmother took the train during the 1910's from Quincy to Seattle &
visited her aunt (which showed up in the census of 1920!). When my grandparents
moved from Quincy to Seattle they traveled along Highway 90 (this was during the
1920's).
Hopefully some of this is of help to you.
Kerry McHugh
Olympia WA