What are the minimal changes to human biology that a biological engineer can make to create humans that successfully reproduce via egg-laying? Assume that he wants to preserve as much of the traditional human biology as possible.
My gut feeling is that an egg with enough energy content to allow a normal 9 month baby to grow inside it would be too large for human anatomy to allow laying it, apart from posing significant challenges in term of gas exchanges.
Therefore the only viable option I see is to have your human lay a fertilized egg, from which a baby hatches after few weeks and is then hosted by the mother in a pouch a-la marsupial, continuously fed while completing the development in this way.
For convenience and practicality sake the egg might be laid in the pouch directly.
To make this feasible in any way, the female body would have to change to make the necessary accommodations for this new way of reproduction. You need to clarify if they can only carry one egg at a time or multiple.
So, if going with one or more, you'd need to alter the hips and pelvis to be wider and the birth canal to be stretcher and more lubricated to allow for a wide birth of the egg, perhaps stronger abdomen muscles to achieve the necessary power to push such an object out.
You also need to determine egg size. That seems to dictate how many your females can carry and how big the womb would stretch. I'm assuming an unfertilised egg would grow to a certain size before it's laid, probably something akin to a chicken, but I'm sure a fertilised egg would act differently if it has requirements
If the fetus inside the egg needs to be carried until a little bigger to be laid then carry out the rest of its gestation or will it be laid as soon as it's fertilised? Which is more optimal for its development?
Not only egg size but is the shell hard or soft? Or would they be birth soft and harden up after birth when exposed to air? Soft would lead to the logical through that would lower the number of changes to the female body, but not by much; it'll just be easier to pass through the birth canal. But softness may be riskier for the offspring if it breaks. A Hardshell would make it much harder to carry and pass but the offspring would have more of a chance
Now, more changes to the female would be how the body can change to the developing attractions; the weight of eggs may differ from the weight of a traditional pregnancy, where you have a lot of water weight along with the actual child.
Would the pregnancy of the eggs cause the normal changes to nest and brood their eggs, to cause them to lactate in preparation for a little hungry mouth(s) or would the eggs emit a pheromone to do that?
All this I believe you have to consider in creating a feasible human-laying species. Mildly adaptable but only you can decide on the fine print. It all revolves around how many, shell-type, and size, the female body can be adapted around that. We don't know what sizes you're looking nor quantity to give a more precise answer