I think this is a great idea, and a good way to show the objective necessity of morality.
My biggest criticism of your outline is that, if you are arguing from a Natural Law standpoint, Natural Law deals only with man, not animals. This is a common misunderstanding which you do not want to perpetuate. Natural Law is based on man’s nature, which is a rational nature. I sometimes say “Rational Law” rather than “Natural Law” in informal discussions, because so many people get confused and sidetracked by this term. Only man, uniquely among all animals, has a rational nature. So Natural Law can only truly apply to man.
With that in mind, you might want to eliminate or greatly reduce your discussion of animal behavior. It unnecessarily complicates the debate and causes confusion. While it is true that some animals sometimes copulate with the same sex, it is also true that they do all kinds of things which humans ought not to - from eating their young to eating their own dung. So what you said in 1.a.ii.1 is the only point I think you really need to make: People, because of their rational nature, are not in the same category as animals. If your friend wants to debate that, that is a separate debate.
Also, you might want to deal sequentially with homosexuality and then monogamy. This simplifies the logical process I think. This would allow you to start with a more basic assertion - such as the necessity of human survival - and expand from there. Even somebody who does not accept reality as the Church perceives it might see the logic in this.
Something like – (1)Sex is undeniably, at least in part, for procreation - (2)which necessitates heterosexuality - (3)offspring need parents - (4)the best parents are those secure in a monogamous relationship - (5)feelings of betrayal and insecurity result from unfaithfulness - (6)this effects the parents and the children adversely - … etc.
I wish you well.
