Spine of the world (more specifically the Silver Marches) would be a good starting point. Given the different types of geography/temperature changes needed it can be difficult to tie the adventure sites together coherently unless you really spread it out across the realms (quite possible given teleportation). While the adventurers may want to pursue the connection between the different Giant modules it would be easier to motivate them using the organizations prevalent in the Realms vs. a single ruler.
Will you be using Eclavdra as written (splinter faction of the Drow) or converting her over to Lolth?
My first thought is to move both houses over to Forgotten Realms whole, since there's an Elder Elemental God that's worshiped by a few drow and other Underdark creatures (Ghaunadaur, in this case, with some details in the Drow of the Underdark book). That would be the 'unnamed' Elder God that they've turned to the worship of. That way I have less to worry about bringing over, and then can explain away their destruction.
I plan on converting it to 5e as well, placing it just after the 5e Starter Set, since [Spoiler Alert!] there's a drow already. Going to change...what was that drow's name...to a female, and change the two doppelgangers into actual drow (probably males), making it so that they're part of Eclavdra's rebellion, seeking to capture the Forge of Spells for the glory of Ghaunadaur (and Eclavdra, of course).
After the Starter Set, there's going to be a little bit of Scourge of the Slave Lords--I am tempted to add that in in it's entirety, since it is a fun little adventure, and I haven't run it in many years, but I am unsure if I want to or not. If its not the entire adventure, it'll be inspired by it; the gist of it is that the drow have set up (in disguise) some bandits to kidnap people for sale into slavery. Most of the kidnapped people are being kept in the bandit's hideout, since they're incidental to the plan. The drow is going to hide while the PCs defeat the bandits, then try to drop the roof of the old dungeon they stashed the kidnapped folks in, killing the party and the bandits in one fell swoop (or, alternatively, have the bandits have a "secret weapon" which is an enchanted jewel that spawns a nasty demon sort of thing that's supposed to kill the party and the bandits--that sounds more drow, doesn't it?).
Assuming the party survives, they return to Phandalin to even more fame. Gundrin (sp?) brings them to the mine and says, "Hey, our first shipment is ready. If you want to make a profit off it, make sure it gets safely to [town A]." Town A is, of course, the location of the giant black spider-orb that Lolth is going to use to enter the Prime Material Plane. That's where I need to decide which town to place it in. I considered Mirabar, but there'd be no shortage of dwarves there, so they wouldn't necessarily need a single shipment of mithril and/or weapons and tools. Ditto any of the larger cities in the area around the Spine of the World.
Thus my conundrum. I don't mind fudging the mountains and saying some of them are volcanoes--that's fairly easy. I'll probably have a sidequest to take them to Neverwinter or, possibly, Silverymoon, to learn about drow, since they'll doubtlessly be curious by then, especially if they discover the drow in the slave part of the adventure. But I cannot figure out, yet, anyway, what city will suffer the touch of the Queen of the Spiders.
EDIT: Come to think of it, I might have to also put in a second side quest, possibly to find the magic McGuffin to fix the Forge of Spells, after the Starter Set is over, because, working out XPs, it seems like a lot to get the party to level 18-20 when they go to finally fight Lolth (a goal I always want when making full campaign; my players and I love it when we get to see our characters all the way to the end, bitter or otherwise).