There is no "split" except at death. The soul is the act of the body.
From this quote it doesn't appear that Rand understood Aristotle's conception of act and potency.
I read your link and I think Parmenides is wrong ("Parmenides had been forced to the position that there is in reality no change at all").
Carrying (from your provided link) Aristotle's thought ... "From being-in- potency there can come being-in-act," and Michelangelo's comment about statues ... a bit further ...
If a statue is the act of the stone, the fact remains that the statue is material from stone.
And so, for the soul ...
If the soul is the act of the body, logic holds that the soul is material from body.
Sounds to me like Aristotle was approaching some truth regarding the mortality of the soul.