Yeah, variety (or at least the ability to generate variety) is always important as conditions change. I was trying to pick starting rules that would have the most obvious impact.

The death-by-pathogen option is a big one. Eliminate it, and things can change a lot. Then it's solely a picture of how to funnel resources to children via any available adult. Homosexuality can play a large part in such a scenario, since adults would be available to provide support without burdening the system with additional children, and their reproductive habits are largely irrelevant (since the disease vector is removed). The species could use its homosexuals as supplemental parents. It'd be a great innovation. :)

Similarly, simply reducing the time needed for a child to mature can have dramatic consequences. Then, even with fatal disease still a factor, promiscuity is very viable since the strategy is to produce as fast as possible before disease takes its toll.

Mind you, all of my "solutions" mean that a species has evolved to behave naturally in the specified fashion. It would not require societal (political, religious) influence to mask inherent urges. Like the albatross, they would behave in a way that is perfectly "natural" to them.