Its interesting that I did not know of this deleted scene, but I don’t think that it would serve the purpose here. Even worse I think it would support Han’s behavior, because it would instantly confirm that Han was right to ignore Leia’s attempt to block him off. In the original scene its open ended, Leia immediately leaves after the kiss and Han is left anxious whether he ruined everything.
Maybe there is a way to remove some of Leia’s attempt to block Han off, so that he pushes her less. but I don’t know how to achieve that.
Another idea might be to have 3PO bust them earlier, cutting the actual kiss and signalize that Han went to far. But this would require a lot more work to pull off as none of Han and Leia’s following interactions support this in any way. Lines like “…, scoundrel, you’d like him” or “I Know” come to mind.
The idea to have Han mess it up and Leia rejecting him afterwards until he pulls himself together intrigues me. But it would require a scene were Han apologizes. Maybe he does so after Leia helps him get up after the stormtroopers throw him into the cell. In addition to that Han could say “I love you” and Leia respond with “I know”. Its actually weird that he doesn’t say it, considering that he might very well be dead in a minute.
On another note I would definitely cut Han holding Leia on his lap.
Other than that there might be some bits and pieces to their constant bickering in the first act that could be cut, but don’t really need to as Han is not really pushing any boundaries, but just asking for a slap in the face (lucky for him that he was only captain, otherwise he might run a risk of being demoted 😛).