I think Soukichi's activities as Skull are being left vague to help reinforce the mystery of the character. That said, it really does gel with other things we know about the canon to say he had the Lost Driver and Skull as long as ten years ago. While the series hasn't explicitly said "Shroud wanted Soukichi to be Philip's partner," I think it's fairly implicit in how certain scenes in Begins Night are shot and how Soukichi is portrayed when he's mentioned in the core W series. W the show consistently treats Soukichi as a sort of super-cool surrogate father figure who left Philip and Shotaro an incredible and sometimes tragic legacy, just as the movies consistently treat Skull as a role model, in many ways an ideal of heroic masculinity that the Shotaro of the series tries to emulate.