So here's the idea:

1. The PCs are goblins, who live in a tiny underground settlement.
2. The settlement is part of a sprawling network of caves, chambers, traps, lairs, etc. inhabited by many (small settlements of) odd creatures.

Various elements of the environment are "off"/artificial:

1. The ecology of the dungeon isn't sustainable, and depends on constant "restocking" by semi-mythical "dungeon masters" who teleport creatures into the dungeon, reset traps, etc.
2. The architecture of the dungeon is a mishmash of styles. Some sections have a coherent theme, but there is no unifying history or purpose tying them together. Sometimes, entire areas of the dungeon mysteriously vanish, are reconfigured, or are enlarged, causing earthquakes.
3. No creature in the dungeon remembers or knows of an external world. The goblins themselves think their settlement has always existed down here - that, in fact, they are the only goblins in existence.

The solution to the mystery is as follows:

1. The dungeon is a kind of zoological reserve/entertainment show/terrarium for a civilisation of trans-dimensional Giants and their pneumatic servant-golems (the dungeon masters).
2. The Giants wipe the memories of creatures introduced to the dungeon, and use scrying to follow along with the conflicts of its inhabitants. This is their favoured entertainment.

The gameplay loop is as follows:

1. Explore the dungeon to help grow and protect your vulnerable goblin settlement.
2. Encounter new PC options by befriending settlements with other races.
3. Discover the truth behind the dungeon and decide whether or not to reveal it to your fellow goblins (easiest)/ personally stage an escape (hard)/ stage an escape for your tribe (super hard)/ stage a mass breakout (next to impossible).

The only difficulty here is that I don't want to write a 300 room megadungeon from scratch. Does anyone have any suggestions as to something that would provide a good framework for this type of play?

You could start with "World's Largest Dungeon" by Alderac.

https://en.wikipedia.org/wiki/World%27s_Largest_Dungeon

Lost City of Barakus is a big, well written dungeon (not "mega" to the extent of Barrowmaze or Rappan Athuk but plenty big enough). Comes in Pathfinder or S&W OSR flavours.

A lot of the upper level monsters are goblinoid already and each area has a good environment description to work from.

https://www.froggodgames.com/product/the-lost-lands-the-lost-city-of-barakus/

Stonehell 1: Down Night-Haunted Halls is big enough and modular enough to suit your needs I'd reckon.

Would Undermountain work or is that too over the top?

Sketch an outline of the dungeon, but don't map individual rooms. The classic versions are either a cross-section of levels like you see in the basic rulebooks of the various early versions of D&D, or something like the D1-2 drow/kuo-toa realms map with tunnels connecting different areas that are effectively levels. The idea is to get an overview of what's where, and how they connect.

Normally you'd have to detail (room to room) the major entrances/exits because that's how everyone gets in/out, but if you're starting inside the dungeon and they don't know about the outside world, you only need to detail the area where the gobs start. Then as they explore, add more detail in whatever direction they're heading. Steal from published maps, free stuff on the internet like some of Dyson's or the Mines or Khunmar, and so on. Geomorphs are a good option, allowing random creation of an infinite variety of rooms.

You don't even need to sketch out the whole dungeon at the start, you really only need an idea of what can be found in the various directions the party might head; at some point, it's okay to just fade out and say beyond this point lies beholders. The whole point of doing a sketch of the surrounding areas is to provide some context and direction, so you know in general what's the next level up, what's the next level down, and major features. That way you can drop hints and rumors, build up legends, give directions to key features, and so on. That makes it easy to remain \consistent as you develop the dungeon further, without having to plan too much ahead.

Doing some "PointCrawl" notation might be the best bet.
Bullet point locations and chain them together by access.
Does anyone Really care about the tunnel details between Points of Interest?