Ground separation is there since the ZX2 but has nothing to do with balanced. Its neither true nor false balanced, its just not an balanced connection.
Here is an simplificated explanation from Sony itself. Sadly only in Japanese, but an auto translation should work okayish.
So even though it may be possible to reduce the crosstalk, it doesn't eliminate it because even though the ground is seperated on the plug, it is one device. You only have one walkman, that means the two grounds will, in the end, share the same chassy and so are finally the same ground again. The device has 1 Master ground that all grounds will lead to. And you also don't have any of the other advantages of the balanced connection. You only have 2 LCs instead of 4, and, of course, much lower output power (1/4)
Splitting up the GND is unrelated to a balanced connection and doesn't replace it.