Simplest solution - kill all the males
You don't really need to do this through extensive genetic engineering, and it will probably happen naturally anyway. And yes, this evolved human form will be very stable. There are analogies in nature.
The Y chromosome in humans is actually very, very small compared to other chromosomes, and particularly useless. It is full of anomalies, that make males much more prone to genetic diseases. Eventually, the Y gene will become so non-functional as to be eliminated completely from the genome.
Sexual differentiation in humans is NOT dependent on the Y chromosome. It is useful for starting the differentiation process, as a trigger for other events, but these events can be triggered by other genes. There is nothing on the Y chromosome itself that is exclusively part of the process, or even that is exclusively needed in the process.
However, by eliminating the Y chromosome, you eliminate a lot of problems associated with testosterone. Particularly, the predisposition to violent behavior, and the predisposition to mental illnesses and mental aberrations that lead to violent behavior. Without testosterone, your evolved humans will be particularly non-violent, even pacifist.
It is not humans per se that are the problems, it is human testosterone-driven after-the-fact ooops-evolution-goofed males. Humans, as first envisioned by the default 'female' setting for humans, the female, are actually quite civilized.
It is no secret that men are basically genetically modified women -
the female being the fall-back developmental pathway for any fetus.
The evolution of the two sexes could indeed be regarded as a
long-running GM experiment. Its legacy has been to endow men and women
with different, and often conflicting, sets of genetic interests, and
to ignite a powerful evolutionary struggle, which has accentuated the
differences between the two sexes. In several respects, the experiment
that gave us men is not going too well just now. Though it is a weary
lament to lay most acts of violence and aggression, from the strictly
local to the truly global, squarely at the feet of men, the
association is strong, consistent and undeniable. Women very rarely
commit violent crimes, become tyrants or start wars.
So to achieve your results, just get rid of the Y chromosome completely.
Incidentally, getting rid of the Y chromosome would be extremely beneficial to a society living in very close quarters underground. Females have always been much better in close quarters-for-prolonged-periods environments.
And getting rid of the Y chromosome is really, really easy. Just kill off all the males, and induce a reproductive 'male' gender by artificially triggering it using testosterone shots in utero.
Hokkaido University researchers have revealed that key sex-determining genes continue to operate in a mammalian species that
lacks the Y chromosome, taking us a step further toward understanding
from How to be a male without the Y chromosome
Second solution - pure hermaphrodites
To alleviate your concerns, at the time of copulation, the participants decide which will be 'male' and which will be 'female', but only for the length of time of the copulation. Then they return to neutral.
Third solution - the earthworm
The hermaphrodites copulate as both males and females at the same time. Each becomes pregnant, each reproduces. This trick has been used in nature. See for instance earthworms and they have been stable for millennia.