I've sort of figured it out. The white flashes are Sephiroth's influence. Zack comes in during the fades to black. Interesting that Cloud whites out after the temple, rather than blacking out, particularly in view of my earlier theory that blackouts are the Zack persona coming into his own, while the whiteouts are the Sephiroth replica overlay taking over.
Yep on Sephiroth, but... Thanks in part to the Ultimania Omega FFVII book, this is directed towards the blackouts = Zack part. It's not Zack. There are scenes in the game that give clues as to who is talking to Cloud. You are close:
The Cloud in uniform goes to Sephiroth. The Cloud in civvies stays put. Interestink. Guess which one represents the Cloud who was overlaid by Jenova.
Cloud in civvies is 'young' Cloud. He helps Tifa in the Lifestream to restore Cloud's memories. Cloud in uniform does appear outside of Cloud in a optional scene in the Honey Bee Inn.