Ooh, faulty wants something played faster? Didn't see that coming..!
The speed is fine.
The fact that you move your hand while playing the first octaves is also fine.
What's lacking in the first octaves is the atmosphere. It's difficult to put the finger on it, but I feel that it's not calm enough. The color can also be a bit more on the top, but it's probably because of the piano and the camera.
Then, the second half of the second bar; The phrasing isn't right. The G should have an "accent" and the E, in the 3rd bar should have a small one. That's the basic line. Notes after the G (f, e) and after the E (d, c) should be played in a diminuendo. Now there are accents in those smaller notes, which is not right. How you treat the long E in the third bar is up to you - either with a tiny bit of time, or with an accent. Both will work.
Then you need to feel the c (the first note of the theme) muuuuch more. It's completely empty, only a c major, without a top note (and fermata!) and suddently this c is coming. It's like you're having a dream, and suddenly you wake up to a much darker reality.
A general thing is that the left hand has to be more melodic. Voice the top of the chords, and not the full chord.
Around 2.20 in your recording, you go down in tempo quite a bit. I like it, and I'd do the same thing. but you need to get back into tempo again, otherwise it's a very dragging place.
To be completely honest, it's not even a melody. It's harmonies going up and down. So once the new harmony is heard, there is nothing more to listen to. So don't make it more than what it is.
Where Alistaircrane4 mentioned the trill, I want to mention the harmonies. You need more direction, otherwise you get stuck. Now, it's not the same as playing faster, but you're tempo is a bit dragging, in general. So don't play faster, but also not slower.
I'll write more later. I need to practice myself
