We have just finished with Caverns of Thracia (COT) and are about to start with Against the Giants (G1-3) (both of which I've palyed and run before). Here's my take on these classics in view of your list.
SPOLIER ALERT
Doug McCrae said:
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1) Variety of monster type while remaining within a certain theme. One doesn't want all orcs, but otoh one doesn't want a total zoo. The four elements in ToEE are a classic example of a theme.
G1 has pretty low monster divesity, what it does have is monsters in concert/in an organic living breathing interplay. Giants enslaving orcs and working with other larger humanoids.
That said, much of Gary's monster placement in the 1e era seems to be completely random.
Not really with respect to G1-3, placement makes sense to me. Guarfd creatures near entrtances. What doesn't make much sense if the lack of effective guards or barriers in G2 and G3. Sleeping guards in G1 stroke of genius.
2) Variety of encounter type - monsters, traps, NPC interaction.
I'd also say (especially in G1, G2) variety of effective appraoches to crwawling the dungeon. If you ignore the recommendation all creatures always fight to the death, also a variety of approaches to overcoming the monsters.
3) Variety of encounter difficulty. For example, the feasting giants in G1 are expected to be far too numerous to be fought conventionally, forcing the PCs to be stealthy, tricky or strategically brilliant.
Same for G2-3. COT is also full of terrain that a clever party can use to ambush and gain advantage over opponents,; especially with the 3 dimensional nature of the caverns.
4) Size. Not too big, not too small. But how big is too big? How small is too small?
G1-3 are basically 2 levels each. I'd call that medium. Half of a G1-3 level would be small, a quick adventure. COT is large but multifaceted, 4 main levels plus at least as many sub-levels weaving in and out.
5) Raison d'etre - the dungeon needs to have some reason for its existence. It can't just be a vast unexplained monster-infested hole.
Does it? The DM should have an explanation should it be needed and to help determine NOC action, but tu the PCs the reason need not be evident.
6) A reason for going? PCs need a reason to go to the dungeon. I'm not sure if this required, maybe general treasure-seeking is enough, without it even being a specific treasure.
Easiest part, just need to know what motivates your players. High adventure sdaring deeds, heroic rescue, loot, mayhem, etc.
7) The nature of the place. Gary seemed to really love temples - ToEE, Hidden Shrine of Tamoachan, Forgotten Temple of Tharizdun. Coincidence? Or do temples to strange gods make for better dungeons?
Temples are good reasons for 5 & 6, and when evil why they are hidden away. Add in the concept of votive offerings and yoo can have a loot fest.
8) Internal conflict. A popular element is a conflict between two or more factions. This is the case in ToEE, Sunless Citadel and the Conan classic tale, Red Nails. This adds both interest and an element of roleplaying as PCs can join one or other faction. Or play each side against the other, Yojimbo style.
Red Nails is a classic, COT lends itself very well to this, with multiple factions. Likewise G1 if you are careful. It adds a dimension to play and options beyond hack-slash (to parley and hack-slash with allies

) Really it adds a sense of versimultude as many a heroic adventure tale includes teh garnering of allies, even if temporary.
SO what you need is a dungeon with a temple, multiple factions, maybe each faction with a sampling of creatures working in conjunction. Add in an interesting layout, maybe a third dimension, that allows for multiple paths through dungeon and use of clever tactics/ambush. Have you looked at Judges Guild's The Dark Tower? It's got all that, plus you can play it with good or evil aligned PCs.