There's a lot of noise in our current method of reproduction - one extra success over 50 years of life is enough to go from a loser to a winner. If evolution had provided a smoother success function, it might go much faster.
What if women would produce an egg, and then every time they had sex, one sperm was selected; from it, only one chromosome would be chosen and added to the forming zygote. A complete zygote would be formed by one woman and a number of men up to the number of chromosomes available. If there were differentation in chromosome function, women could even do manual genetic engineering by selecting the right man to provide the desired chromosome.
A dedicated child would be one where the woman only received chromosomes from one man; the opposite would be a child with many different partial fathers. A society with this happening would allow many more types of social relationship, and would have a huge number of words for relatedness. Perhaps the mayor of a town would be partial father of every child, just as a way to secure his loyalty?
The human problem is that there is no way to have a partial relationship with someone - you are either naturally related by family, or extremely related to them by having children. Establishing these relationships takes forever.
With partial reproduction, each sex act wouldn't be nearly as important; we'd be more like lions.
What if every chromosome had a visible expression somewhere on the body. So, the lips were completely controlled by chromosome 3, chromosome 4 controls the shape of the birthmark which appears on everyone's shoulder, etc. Then, you could easily see which chromosomes had been contributed to each child.
In Rudy Rucker's ware series, synthetic sentient beings (either robotic or biological) spend most of their time searching for the right resources to complete the physical construction of their child.