Fortellings are capitalized but channeling is not. Everything that is "magical" isn't always capitalized in Jordan's work. I think the reason the Voice and Singing is capitalized while seed singing is not, is the same reason that channeling is not but Forelling and Travelling are. They are common words that are representing extremey special and rare abilities. The capitalization is to differentiate. The seed singing is an festival, so it is not capitalized.

As for darkmookster's example... What proof is there? They sang a ritual song that would have been symbolic of their former way of life to a man who had forgotten it. That doesn't mean it was a different song. Are we assuming the Aiel who believed in the way of the leaf, complete passivity, would have a song to detain, or defend or attack an Aes Sedai? Not bloody likely. They sang the seed song, pure and simple.

What we have proof on is there is a Voice and Singing. We know of ONE song for sure. It is the seed song. Anything else is pure conjecture. You may REALLY REALLY want it to be true. But s a wise man once said, "Wish in one hand and crap in the other and see which one fills up first." Let's stick with the facts here. To use an Randland example. The Seanchan are obsessed with finding the "secret weapon" the Aes Sedai used to blow up a huge area, when all it was, was Aviendha having trouble untying a gateway weave(if I am not mistaken). The point is when you guess beyond the facts, you get out on a limb. I suggest we work with what we know.
I can't say whether or not the song will be found or if more nym will be found/made. I can say, I believe there is one song. The only one named in the whole book. Heck, we don't even know the Aiel outside the city gates weren't singing the latest Lady gaga song. Obviously they weren't, but since they didn't specify, we are just guessing what the song was. While my, intentionally silly, guess(lady gaga) is obviously wrong, it doesn't involve introducing a whole new series of powers and abilities to the novels. Yours does.
Lastly, I was a science major in school. This seems like a great time for Occam's Razor. All things being equal, the simplest one is true. (the one that doesn't involve a myriad of songs when we only know for a fact ONE exists) or as they say in medical school, "when you hear hoofbeats: think horse, not zebra"
That is all.