"The Hombu Dojo websites lists six US organizations that have Hombu recognition: Aikido Association of Northern California; Aikido Tenshinkai Federation; California Aikido Association; Makoto Aikido Kyokai; Takemusu Aikido Association; United States Aikido Federation."
That doesnt have anything to do with with IAF. Each country can only have one representative organization in the IAF. The USAF is the current organization representing USA in the IAF. Our own Mr Goldsbury is the president of the IAF. He would be the one to go to about questions about the IAF.
As for Birankai, Chiba Sensei started his own international organization independent of Hombu and USAF. Where as all testing grades are given thru Birankai. But Birankai will assist members wishing to receive Hombu certifications as well.
Here is the link for that info http://www.birankai.org/BirankaiInternational.htm
As for the USAF a lot of growing pains and secessions in the past year. It will be interesting to see what becomes of it all.