I find it interesting that there is a concept of "these songs need AMVs" because for myself, concept synthesis is totally organic. I hear a song, I know the anime. It may take years, even decades, I suppose, for me to hit on the right combination.
My current project involves I song I've been listening to my entire life... and yet it just recently "gelled" with a given anime in my mind. There are lots and lots of songs which could be used in AMVs in the technical sense, but it's definitely a case of not wanting to rush the process and end up with an anime which doesn't fit as well or at all.