I've got a few tips for you.
1. Don't square the cards and then do the pass afterwards. Do those two things simultaneously. In the context that you're doing the pass here (after closing a spread), the pass is supposed to blend into the squaring action.
2. Keep your top hand still. At the moment it basically follows the movement of the packet coming up on top, but it doesn't need to release its grip at all.
3. Keep your lower hand thumb on the side of the deck. If its stretched across the top of the deck then it's going to have to move out of the way and that just adds unnecessary motion to the move.
My general advice would be to practise alternating the real (genuinely closing a spread and squaring) with the artificial (using that action to cover a pass). You'll know how well you're doing by how similar the two actions look and feel.