This is a great question, and it may be that my Elizabeth is a little quicker to forgive than canon Elizabeth would be, but there are some reasons for it, which I will try to explain.
First of all, as you say the background here is a bit different. There is no Jane and Bingley separation to embitter her--in fact, she gets to see her sister's happiness every day--and although she's heard Wickham's story it didn't affect her much, because she didn't trust Wickham, and she only heard it second and third hand anyway. What that leaves her with is a month of proud, disagreeable behaviour in Hertfordshire followed by his proposals and the fall down the stairs. The last, of course, is a very dark mark against him, but there several things here that influence her towards forgiveness. The first is Darcy's own apology, which was humble and sincere, and I do think that Elizabeth has that kind of warm nature that can't help but respond to such things. He's been as good as his word too, and his behaviour during all the weeks she's been in town has really calmed her and helped lower her defences. She doesn't feel threatened by him any more. And again, the humility he's shown towards her ever since the wedding has gone a long way to counteract the impression of his pridefulness which she gained during the first weeks in Hertfordshire. She has not forgotten his early behaviour, not by any means, but she sees that he is truly contrite over what he did, and has apparently made a real attempt to reform his character as a result.
Another factor that influences her here is the simple fact that she and Darcy are now part of the same social circle. They see each other a lot, which makes stiff formality really quite inconvenient. And she loves Charles, and Darcy is Charles's best friend, plus she knows it will make everything easier for Jane if she and Darcy are getting along. That's a lot of what she's thinking of when she tells him that she thinks they ought to be friends. She's not telling him that she wants him to court her, she's just saying that it will be easier and better for everyone if they try to forget the past and behave like normal people around each other. Then when he makes his quiet declaration, how do you respond to that? How do you behave coldly toward someone who has apparently loved you, against all hope or reason, for months?
And that brings us to the last thing inevitably influencing her. As Elizabeth thinks in the original -- "
That she should receive an offer of marriage from Mr. Darcy! that he should have been in love with her for so many months! -- so much in love as to wish to marry her in spite of all the objections... was almost incredible! -- it was gratifying to have inspired unconsciously so strong an affection." What woman in the world would not have her vanity pleased by finding herself in such a situation? Certainly not our Elizabeth.