You've already noted some good stuff here.. I'd say Plato's allegory is definitely a foundational theme of the first Matrix film.

Then you have your observations on the actual word "matrix".. like you said a womb, an illusion (maya), like matter, like a 'Mother of Illusion/Matter'. Instead of the master, she is the mistress.

[From Dictionary.com's origin of Matrix]:

"Middle English matris, matrix < Latin mātrix female animal kept for breeding ( Late Latin: register, orig. of such beasts), parent stem (of plants), derivative of māter mother

This idea of a single female giving rise to life shows up continuously. No doubt you've heard the epithet "Mother of the living" attributed to the Biblical matriarch Eve before, but it goes farther than that.

There is the primordial Egyptian sky goddess Nun, or Nunut, who is said to receive the Sun god, Ra, through her mouth & birth him out her womb every morning.

"Ancient Egyptians envisaged the oceanic abyss of the Nun as surrounding a bubble in which the sphere of life is encapsulated" [Wikipedia]

She has been called the 'Mistress of all', & is most commonly depicted as a nude woman arching over the Earth, her dark body made of a web of stars, seen as the literal matrix of the Earth.. or as a cow. She was the literal foundation of reality & the barrier between the Order of our physical world & the primordial Chaos out there from whence we came.

There is a parallel in ancient Sumerian mythology where the goddess Nammu is seen as:

"the Goddess sea (Engur) that gave birth to An (heaven) and Ki (earth) and the first gods, representing the Apsu, the fresh water ocean that the Sumerians believed lay beneath the earth, the source of life-giving water and fertility" [Wikipedia]

They also saw this feminine ocean of stars encapsulating the Earth, as a womb. The watery Abzu, or Abyss, that void from which all we know originates, even the stars, for they are matter, illusion; born from the 'mater', the mother, the vast emptiness of space..

"It is she who has the idea of creating mankind, and she goes to wake up Enki [her son], who is asleep in the Apsu, so that he may set the process going" [Wikipedia]

I thought this last part was interesting considering a large part of the first film was about Neo waking up from the illusory world of the matrix. Perhaps the Mistress, mother of matter/all that is', could be calling out to Neo from beyond the physical world, & therefore beyond the matrix, which is like a womb, within her own womb.

This 'great mother' figure beyond our reality, seeing Neo as a son, helps him find freedom, leading him to the truth that will result in his rebirth. She does this first by sending a messenger, Trinity, the woman whom he will fall in love & then Morpheus. Their names & characters obviously carrying their own symbolism; they bring Neo to a woman whom we see is an Oracle. This motherly figure that sees beyond the limits of the matrix, hastens his awakening by sharing the ancient axiom of the Oracle of Delphi:

In English: "Know Thyself"

The Matrix film definitely pulls from a lot of old concepts.. In buddhism:

"Maya is the name of Gautama Buddha's mother" [Wikipedia]

Enki btw, is a Sumerian saviour god & the son of Nammu, said to have come down from heaven, then create man from his own DNA, & warn him of the coming flood which would wipe out the species. He chose to help a small number of humans survive & build a new world.. much like Neo sees the role of the One playing out in the second film..

So.. to your question of "Does he ever really escape the cave?"

I'd say we have to move onto the second film in the series, The Matrix: Reloaded. This film continues the themes of the revealing mother figure & question of free will, which would be too much to put into this already long comment.. but I will say it pans out much like @Leaky20 says

"truth is just another illusion - another layer of the matrix"

So, I'll leave it there, thanks for a great post @Apolymask, I learned a lot :)