I know he is writing mainly to correct Elizabeth's impressions of him. But, do you think he still harbors a hope that she may accept him? Is there evidence for it? Or has he completely given up hope?
He leaves rather abruptly after the letter, not giving him a chance to see the effect his letter will have. I know the departure has been planned, but has already been postponed, so why not postpone it longer? If he can bare the pain of seeing her again to deliver the letter, he can bare the pain of accepting her apology.