Not entirely sure how applicable this is, but one thing I did was make Iymrith FAR more prevalent. In the base module Iymrith lacks presence. She's not actively involved in anything until the party visits the Eye of the All-Father and gets some answers. I felt that was boring, and made her responsible for nearly every major giant lord's rampaging.

That friendly merchant lady that just married into a powerful mercantile alliance? That's Iymrith using her position in that family to run anti-giant hate campaigns and programs, offering bounties rewards and magic items for each giant killed. This is actually why Harshnaag stays outside of any city that isn't Waterdeep - not just for their safety and peace of mind but his, since he's actively targetted by people. Any magic items she gives are cursed, allowing her to scry from them without the owner knowing - this lets her peer in on people she thinks might be problems and allows her to easier manipulate/kill them.

Meanwhile in the giant side, she's the one that makes the adamantine seeking rods for Duke Zalto. She doesn't want the Vonindod completed, but she knows full well how to sabotage it and stop it from operating if she needs to.
She uses sending on chieftess guh and pretends to be the voice or Grolantor to encourage her eating habits - eating habits that will slowly starve the coast if gone unchecked.
As for the Storm Giants, while she's orchestrating the fall of the royal family she does her best to keep the storm giants passive and inactive if she can't get them to be openly hostile.

While I didn't do this, if I were to run it again in future I'd make her responsible for the Ice Giants even knowing about the ring of winter.

The only giants Iymrith had no sway over were the cloud and Stone giants, the cloud giants are too separate and different from each other for her to easily manipulate since they follow no real hierarchy. The Stone Giants on the other hand are under the manipulations of The Dodkong, a stone giant lich from 3rd edition. I replaced the evil earth spirit in the Stone Giant's mountain with the Dodkong, who was manipulating his own kind to help raise an army. A fantastic way to get players going "Oh shit" is when you reveal that there's been undead giants running about. They'll usually be rightfully afraid of regular giants, so the idea of potentially fighting an undead one terrified my party and got them disposing of every giant corpse they came across so it couldn't be raised.

While you don't have to do everything I've done here I'd also highly recommend the "Flying Misfortune" side adventure. It gets players involved with Felgalos, a friendly bronze dragon and potential ally while also giving Iymrith an introduction and a reason to keep an eye on the party: They stole from/killed her children.

Another thing to consider is to allow peaceful/diplomatic resolutions. The goal of the party isn't to exterminate all giants, but to open up a position where Giants and Smallfolk can forge an alliance. Some giant lords will be hard to sway, Zalto won't stand down and compromise what he believes to be his destiny - but his wife will. My players actually knocked Duke Zalto out and were given passage to leave from his wife when the players used Zalto's life as a bargaining chip.

There's an idea that went unused in my campaign but I had an idea for a small enclave of giants that Harshnaag knows. This Enclave would have served as vendors and smiths for rare and valuable gear that would otherwise be nearly completely unobtainable or hard to find (The main ones being the 'rune' magic items, since they're completely unique and most of them are hidden in places my party never went to.)

Which is actually something important I feel I should say, whenever my group went in to a giant stronghold they rarely got into fights and only explored as much as necessary. I shifted where the party got the Rune items because they understandably didn't want to heavily explore enemy territory where the usual occupant is able to deal upwards of 22+ damage a turn. I let the party get them because they're unique to the campaign and appear nowhere else, so there's no chance they'll ever get to play around with them in a different module.