I'm not feeling that the neck wood of a Wal impacts meaningfully on that legendary tone. It's there, in spades, on every Wal i've heard, be it rosewood or ebony, and the almost infinite natural variation in the maple and laminates used. The weight range alone tells you how much the wood varies, but the tone remains. The only thing we know never changes is the pickups. For me, so much of the tone is from that recipe, fine-tuned by the preamp (but the tone is still there passive).
Your bass sounds good in that video, but as you say, it doesn't really have much essence of the Wal character. I hope it works out, but i'd be astounded if a neck change brought you much closer to the Wal tone. Watching with keen interest if it does!!