My area of study is cross-cultural differences. In some cultures, it is considered inappropriate to “give a gift” (as you suggest in your forgiveness process). It is considered inappropriate because such gift-giving is seen as a sign of superiority. So, might it be best to skip this step in your forgiveness model for some cultures?
In such cultures, as you say, it is best to give the gift in ways that respect the norms of the culture. One need not give a gift within a box all wrapped up in gift-wrap and a bow. One can be more subtle about it: a smile, paying respectful attention to the other, not speaking badly to other people about the one who hurt you. A gift is a generous and often unexpected kindness which can be done tastefully by knowing the norms of a given culture.