Starting the piece with rubato = cheesy! It should just shimmer into view, like a veil being lifted. The beauty comes not from melodic rubati, but from the sound quality.
In the left hand, pay more attention to the long line, not just isolated bits.
I actually like the large amount of time you take before the second theme area.
I don't think your interpretation is totally consistent. You play it in a generally subdued, intimate way, which works, but then towards the end you add some low octaves, which cancels out the effect. It just doesn't go along with what you have been doing.
Sounds like you have good fingers!
Walter Ramsey