When davening at different synagogues, I notice that some use different melodies for songs (eg: El Adon, Hallel, L'kha Dodi) as well as different nusach (in the sense of melodies for brachot used for the type of day it is) even among synagogues that all consider themselves Ashkenazim. I assume that some of these differences are descended from differences that existed in Europe. I am referring here to differences that seem to be intentional, not those from a shiliach tzibbur that cannot carry a tune or doesn't know the correct nusach for the service. You can also hear these differences when a shatz that was raised in a different community leads a service. When asking once such person, his response was "Well, you sing the melody that you learned as a kid, in my case in Chicago."
My question is, can anyone recommend a good book that lists or explains the different melodies that are used in different communities, ideally with sheet music. For example, I would like to learn that xxx prayer was sung with this melody in Vilna, but this melody in Volhynia, and this melody in Frankfurt.
I would like to request some books like this on an interlibrary loan from a college or cantorial school. Any suggestions would be appreciated. Some of the books that I have found locally have arrangements by specific composers, sometimes for choirs, but that is not really what I want because (correct me if I am wrong) I do not think that represents what would have been heard historically in European synagogues.