He proffers several possible stand-ins from published works, mostly looking for something that brings the action back to the material plane and involves more drow, even postulating a possible civil war. It's an interesting idea, but I wanted to explore it a bit in light of what we know Q1 was originally supposed to be.
I've discussed this before, in the context of the Temple of Elemental Evil and possible tie-ins between the two adventure lines, but in a nutshell, the original Gygaxian concept for Q1 had nothing to do with mechanical spiders or invasions of other worlds. It dealt specifically with the god of the Eilservs, the Elder Elemental God (EEG). Indeed, it was the worship of that eldritch deity, rather than Lolth, which set the whole chain of events in the Giants series of modules in motion, and most specifically set the vast majority of Lolth-worshiping drow against the renegade EEG-worshiping faction led by Eclavdra Eilserv.
Originally, the module was supposed to set up a possible confrontation between Lolth and the EEG, as the players attempted to complete the latter's banishment to "a distant star":
I had what I consider a much more interesting plan for the conclusion of the G-D series, one in which the PC party could loose the Elder Elemental god or send him into deeper isolation, thus assisting Lolth to become more powerful. By very astute play, they could have thwarted the designs of both evil entities. The Demonweb Pits were indeed envisioned as maze like, but there were to be no machines therein. -- Gary Gygax on EnWorld, August 2006So in Q1, originally, the PCs would either help Lolth by increasing the shackles on the EEG, free the EEG inadvertently, thus setting the stage for a final confrontation, or thwarted both. Players being players, that last outcome is doubtless unlikely in the extreme. Ahem.
But this does give us an intriguing idea as to what a potential Q2 might have been. Assuming that "Q" in the name refers to Lolth as the "Queen" of the Demonweb pits, what we inevitably end up with is the ultimate climax to the adventure as a whole; a showdown between Lolth and the Elder Elemental God, with the PCs being at the exact point of the balance between the two, trying once more to thwart both mighty beings, possibly by playing one against the other (that's how I'd set it up, anyway).
This also works with the larger meta-narrative that seems to have been originally intended for these modules. If the low-level T1 was the start of that meta-narrative, and Q1 (or a hypothetical Q2) was the capstone, that leads us from Hommlet to the Temple of Elemental Evil (first introducing us to the EEG, although not in the published version), to the Lost Caverns of Tsojcanth and the Forgotten Temple of Tharizdun, to the three "giants" modules, to the Descent into the Depths of the Earth series, to the final confrontation with both Lolth and the EEG, who are the true protagonists behind what's been going on all along, and who are at odds, as Lolth was either responsible for the EEG's original imprisonment, or for his continued confinement by her protection of the keys to his release in her Demonweb.
A drow civil war would certainly be possible in such a scenario, as the newly resurgent EEG would be able to flood his followers with power, while the followers of Lolth would be scrambling to contain them. The PCs, flung back to the Vault of the Drow after their misadventures in the Demonweb Pits (having inadvertently freed the EEG) would have to deal with the mess and try to defeat both. It's entirely possible that the conflict would have the PCs going far afield; maybe even returning to the Temple of Elemental Evil, or the caverns beneath the Fire Giant's hall or the Hill Giant Steading, where shrines to the EEG still exist.
Basically, Q2 would be a second chance for the PCs to stop both Lolth and the EEG, if they failed to do so in Q1.