1: Xilmi's Brutal AI, you can apply it along with other mods.
2-3: I don't think I have yet seen a megamod which doesn't add more intermediate-tech content. And most of the more developed mods also add further advanced tech. These are something of a given.
4: Hybrid mods are hard to come by currently, however they do exist.
- Apparently XCF has underwater bases, according to one of the comments here?
- I think Piratez was trying to head in that direction though I am skeptical it ever got there.
- The Hybrid Mod by Precentor Appollyon is an unfinished abandoned project which is technically a functional hybrid mod but it is buggy, underdeveloped, and lacks direction.
- The Hybrid Mod Megamod by Mutantlord is a project attempting to combine Precentor's Hybrid Mod with Hobbes' Terrain Pack, Reaver's Faithful, The World of Terrifying Silence (TFTD), and Final Mod Pack. I don't know very much about it yet but it is probably early in development. And given how ambitious it is, odds are it'll never truly finish.
- Community Map Pack has a hybrid globe and you can load it with another megamod, but it can cause conflicts and also you won't get very much use out of it if the primary megamod doesn't make use of both land and water features.
>> Most megamods simply don't have that yet, as until relatively recently nobody had even successfully made a proof of concept of the hybrid capability.
5: Plenty of mods have a sophisticated and well-developed story. But what do you mean by both cyborg and psi lines? It sounds limiting and like something you're unlikely to find outside of Piratez, XCF, 40k Mod, and maybe From the Apocalypse or Area 51.
6: Combat shields for soldiers show up in a few mods. I'm not well-referenced on the specifics but the following mods may or may not contain them: Piratez, From the Apocalypse, 40k Mod, XCF, FMP, TWoTS. Other mods probably do not, for the most part. Reaver's Harmony has shields on aircraft and alien spacecraft but not on soldiers or alien units.
7: Most mods don't really expand the map sizes above Vanilla. Some mods which I know contain larger maps are Piratez, XCF, 40k Mod, Harmony.
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If you want something which matches all of these, the closest I think you'll get is X-Piratez with Brutal AI. It likely doesn't have proper hybrid integration and underwater bases but I think it might contain some earlier iterations of trying to push the concept. X-Piratez is a total conversion which takes place far in the future after the first war ended in defeat: the aliens took over and the world is drastically different. The mod combines serious and silly elements, and at least according to some people, it is filled with dangerous levels of boobage. This is the largest mod in the community and contains tremendous amounts of content, with nearly every feature which existed during its development (and some that didn't) present in the mod.
If you're willing to let go of hybrid integration, shields, and/or cyborgs, then there are more which I can recommend to you:
40k Mod is a total conversion set in the Warhammer 40k universe. The mod is well developed and features some of the most advanced use of OXCE scripting features I have seen yet. As a player, you will be able to do many things you can't do in most other mods, such as place a soldier inside a larger combat vehicle or use a bipod-mounted weapon.
From The Apocalypse is or very nearly is a total conversion which takes place at approximately the timeframe of the alien invasion during X-Com: Apocalypse. This mod is only available from the forum. It features tons of original spritework done in the style of Apocalypse as well as many items, techs, aliens, etc. which may be familiar to anyone who has played Apocalypse. But it goes well beyond simply recreating Apocalypse but rather greatly expands upon the concept. It is currently a work in progress but it has been in high-paced development for quite some time and it is in a high quality and very much playable state.
The World of Terrifying Silence is the only big and popular TFTD megamod in the OXC modding community thus far (though one or more others are in the works). It is designed in the vein of the original TFTD but greatly expands upon the concept and adds many new and terrifying enemies and things to encounter, maintaining the theme of being loosely based on the C'thul'hu mythos.
UNEXCOM is a megamod which re-imagines the alien invasion as having taken place during the Cold War, and thus the available technology as well as the political scene is significantly altered. The politics side of things also takes a more significant role in UNEXCOM than it did in the original game. In addition to this, the mod features many improvements and diversification of options and gameplay. It is not as strongly story-directed as some, but it has a distinct focus. It is complete but not fully polished, though it is fully playable and should be generally bug-free.
All five of these mods are well-developed and story-driven for the most part, and in my opinion stand above the rest of the community in terms of offering fresh content and a unique feel. There may be others which would fit here as well but which I am just not familiar with.
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My own mods Reaver's Faithful and Reaver's Harmony have been mentioned here already, but I wish to clarify:
Harmony isn't what I would say offers a sophisticated story-driven experience like the five above. Much to the contrary, its sophistication of story is in cleaning up the haphazard mess of the original game's story and polishing it up into a more cohesive hard science fiction narrative. Based on what players have told me, Harmony is arguably the most well-polished and well-balanced megamod in the community and it offers more-or-less the feel of the original game with expanded content and a better grasp of gameplay mechanics. It is also a much less frustrating experience than most (where XCF is known to be arguably the most frustrating megamod), though the predictability of gameplay has led at least some players to find it easy even on the hardest difficulty. (Harmony also greatly extends the difficulty range from Beginner through Superhuman.)
Faithful is an earlier step in the development of Harmony. It exists at a point in which I chose to add far more unique content than I had originally intended, and that is why I switched development to the name Harmony, because I knew several players would not appreciate the new direction. Faithful is, as named, more faithful to the original experience. It is well balanced, pretty well polished, and generally complete but simply with less fresh content. It is, more than anything else, the original game but way less broken. To that end, Faithful still has plenty of fans who prefer it over Harmony.