Thanks for the web site link. It gave me a lot of background about the immigration/naturalization process. I'm going to try to get some of the microfilm at my local FHC.
Were you not able to find your great grandfather's name on the Germans to America series index? It should cover the time period you are looking at. There's also a Russions to America series covering the same time period -- our ancestors were from Prussia, so we looked there as well.
Good luck, and thanks for your input.