When I say "Underdarkish" I mean "Vast underground tunnel networks and collapsed caves".
Not "Menzoberranzan"
Though I definitely understand your trepidation. The Underground area should be just as barren and terrible as the rest of the planet, housing only horror and death in darkness.
And yeah, I was thinking of having it in/under the Black Spine mountains be just the thing. A depressing hole in the ground full of slave labor and cruel overlords who force those unfortunate enough to be their victims to dig and search and scrape for the Gith's way home, trapped in the mountains by a collapse, the location lost to time...
Play up a sort of Caste Society wherein the "Original Gith" are still powerful and immortal with metal weapons, while the everyday gith are corrupted by the wasteland and magic, as well as possible issues with inbreeding or crossbreeding with only partially-compatible species (Since the Gith are aliens)...
Could do a whole Valusians thing with the gith in that version of the setting. In the Hyborian setting their society broke down when the dinosaurs came and while they tried to infiltrate human society to control it, repeatedly, the serpentfolk wound up slowly degrading themselves by interbreeding with humans, inbreeding themselves, and generally losing all that they once were. In Conan Exiles you actually kill one of the last "True" Serpentfolk called "The Degenerate" because even he is actually a twisted mockery of what the Serpentfolk once were.
Definitely wouldn't want them working with other Sorcerer-Kings or having an "Advanced Society" with plenty of food 'cause it kinda goes against the core conceit of the world being royally screwed up and a handful of wealthy people controlling almost all the power and arable land. Especially not with letting people go, either.
And then, once the portal is found, you can grab that dusty copy of the Black Spine Mountains off the shelf and run it in 5e!
(Though I was kinda going at it without Nibenay being the driving force to unleash the "True Gith" on the world)