Well, lucky you, I happened to still be on the site when I saw your question that I know very little about, answer-wise. The only reason I'm responding to waste your time is that I remember reading in more than one motorcycle magazine review (when the bike first came out) that "Valkyries use the same alternator system as GWs". The reason I remember (and keep in mind, I don't know whether or not he was accurately informed or not) is because of the writer's specific comment about it. He said, (paraphrasing from memory) "and because Honda decided that it made more sense, cost-wise, to just use the same alternator as the GW (vs. one made specifically for the Valk) owners can probably add whatever accessories their hearts' desire as it was built to power a GW with all of its bells, whistles and lights. And more lights."
I still have the original battery in mine and I've been amazed that, even after cold Illinois winters in an unheated garage, and with no battery tender, the bike fires up strong each and every day I've wanted it to. Maybe you got a less-than-optimum battery in yours? Something you maybe added (electrical accessory?) that isn't grounded properly or is draining somehow? I've wondered about Lithium bats, too, and was going to buy one when mine died, but now I'm curious if my original is going to make it through another winter! Good luck, and sorry to waste your time. But now at least you won't feel ignored!