A bit of googling and wikipedia searching has pointed me in the direction of a few new ranking sources. The key piece of the puzzle was the Aggr Ranking, a German website that hosts an aggregate ranking of FIFA's rankings, and some of the familiar alternatives like Elo, Ziaian, and AQB, as well as three others that are completely new to me:
The Roon BA is in English and provides a ranking, although no date, nor does it specify its method. It seems to be fairly in line with most of the more reputable lists. A women's international ranking is also available at this site.
Xocca is a German ranking and, besides the difficulty of trying to decipher country's names in the Teutonic tongue, also seems to be a respectable list. The method is provided, or at least sketched, but since my skills in German consist of looking for words I recognize from Dutch and filling in the blanks with semi-intelligent guesswork, I won't take the time to try to explain it right now.
Lastly, there is Bull's Fussball Weltrangliste, again German, but perhaps not quite as sound as the other new kids on the block. The top of the list looks OK but, even though I maybe biased, no ranking should have Canada (or should I say Kanada) at 109. Again, the method is explained, in some detail, but for now I'll leave it to my readers to figure it out.
The existence of these previously-unknown-to-me rankings leads me to believe that there are several more out there that I haven't found simply because they are published in some other language. I can do some French and Dutch googling, but beyond that I don't have the linguistic skills to find more. Any help is much appreciated.
update: Check out the sidebar for permanent links to some of the above-mentioned rankings.