Your query stated, "I sorely need some sort of index to the immigration/naturalization records, but I don't believe there's one out there." You are probably right!
However, the NARA website has some guidelines for searching for these records. They MAY be of help to you. Each state/county has its own system.
Some county clerk's offices and/or county court clerk's keep the original logbooks that recorded such court actions in their offices. (Whether or not they will allow you to search them is another story. I ran into one situation where the clerk's offices are separated from the public by locked doors. You have to ask the employees to search the books for you, and of course, there is a charge. So much for the "Freedom of Information" deal.)
One county I searched in NYS allowed me to search the books, IF I knew certain details. Fortunately, the County Historian had already prepared me with the necessary information, and I was able to find the "Declaration of Intent" to file for naturalization. I have yet to run down the location of the actual naturalization document, although the 1900 and 1910 censuses state that my ancestor was naturalized.
Good luck with your search!