This is why I just stated that the fusion is up for speculation as it's unexplained. Your theories are fine and sound. However some claims are not.
Tensa Zangetsu, or Young-Man, as of right now is Old-Man. Old or Young, neither is the source nor manifestation of Ichigo's Shinigami powers. Based on current information, why would a fusion be needed in the first place? If Young-Man is in anyway part of or a manifestation of Ichigo's powers, then why would Young-Man need to fuse with his own Shinigami powers for Final Getsuga?
Based off the past and his own admittance, Old-Man has always needed Hichigo to show Ichigo his Shinigami powers. Young-Man now needs Hichigo in order to show Ichigo the Final Getsuga. I think a mistake people are making is trying to apply past knowledge to the present instead of apply present to the past.
"Yes, Whitey fused with Ichigo's Shinigami powers and via the release of recent chapters we know that he is also Ichigo's Zanpakutou "Zangetsu". However, despite the fact that he fused with his Shinigami powers, Whitey is still a separate part of Ichigo's shinigami power (his hollow powers). It makes sense that his hollow powers manifested itself apart from it's shinigami half up until the point where they had to rejoin to teach Ichigo the Final Getsuga. "
I'm not sure what your referenceing to by saying that Whitey fused with Ichigo's Shinigami powers. The only way I can see this being true is before Ichigo was born, other than that Whitey is the source of Ichigo's Shinigami powers. Hichigo/Whitey never manifested itself apart as the Hollow powers, because they are Ichigo's Shinigami powers. The true reason to why the fusion happened is still unknown. What is known is that the Hollow and Shinigami were never seperate because the Hollow in Ichigo is the source of Shinigami powers.
"- What I'm saying is that Whitey and the Young Man are the same being but at the same time they are not, they are linked but at the same time can appear apart from each other. If the Young Man really is the manifestation of the shinigami half then it is completely possible for him to release a Getsuga Tenshou whilst appearing apart from Whitey. I believe that prior to Final Getsuga Tenshou, the Young Man and Whitey were both Ichigo's Asauchi known as Zangetsu but more unique than any other Asauchi to date. Both are the same Asauchi but at the same time they can be apart from another each representing one part of Ichigo's power: Shinigami and Hollow."
I understand what you're try to say and I agree with the different aspects of Ichigo's power. But as I just showed via chapter 411, Young-Man is Old-Man and the Old-Man in chapter 541 just made it clear that he is not the source nor manifestation of Ichigo's Shinigami powers. You say something is possible, meaning it never has happened. Old-Man never used nor tought Ichgio any of his current techniques. This is also revealed in chapter 541. Chapter 540 showed that Whitey is Ichigo's only Asauchi, hence why Whitey only appeared. Old-Man is not Zangetsu: chapter 541.
Old-Man has stated he lied and he is not Zangetsu.
Hichigio: has already claimed a few times that he is Zangetsu.
Hichigo is Zangetsu. Zangetsu derives from Engetsu. Engetsu derives from Shinigami (Isshin). Zangetsu is a Shinigami. Hichigio is a Shinigami. Hichigo was created from Holowfied Shinigami souls. Ichigo's Hollow Powers are his Shinigami powers. Thanks to Aizen there is no seperation with concerns to Ichigo.