I like this... I find it very sound.
I always thought it was either this, or "The Hero's spirit split somehow based upon the split in dimensions and differing experiences." If you define a "soul" as "the sum of our experiences," of course it's going to be different in a universe where one is slain vs. a universe where one lives on and has new experiences - much like a chicken soup, the base might be the same, but you come up with different things with the stuff you put into it. I always thought it could be that the Goddesses preserved just a whiff of the Heroic Essense to bestow it upon the Hero of Winds even though the last Hero was experiencing and suffering elsewhere in different dimensions.
Then there's this odd little fanfiction of mine that takes Smash Bros. into account.
"The Continuity Game." I KNOW IT'S NOT CANON - that's the whole point of fanfiction - to do things the canon wouldn't / to put your own spin on things. I wrote it as something of a "what if the Smash universe got involved with the Zelda timeline?" I used the "splitting of souls because of different experience" thing. I also used that story to attempt to solve the "You are the Hero of Time reborn!" line from Ganondorf in WW. Again - not-canon, not even an actual theory of mine, just me having fun with my laptop keyboard.
From a purely logical standpoint that doesn't require the fanfiction writer's leaps of imaginiation, your theory here is very sound, BR. You put thought into it.