1. Restrict the size of the map
The given Sword Coast map is too big, and the given quests force characters to journey to extreme ends on glorified fetch quests. It's better to restrict the campaign area to the region shown in Harshnag's map, which is more or less bounded by the ancestor burial mounds. Even this is a bit too wide, as it includes the cities of Neverwinter and Luskan and some of the Sword Coast., but the players might want to journey to such iconic cities themselves, and to restrict the map further requires moving some of the burial mounds.
2. Put the Giants in actual war
There's a beautiful two page art spread of a Storm Giant and a Fire Giant about to clash, but this event never occurs in the module. In fact, beyond assaulting the initial towns in Chapter 2, the Giant Lords don't really do much of anything except waiting for the players to show up. Instead of that, the main goal of the Giant Lords should be changed to fight the other Giant Lords. The purpose of their incursions into settled lands is to expand their territory and take such from the others. There should be opportunity for frequent clashes between true Giants and their armies, with the small folk caught in the middle. That prospect seems far more terrifying as a plot device than what's written in the module.
Where to put the Giants' war
Chapter 2, the assault on the towns should be the beginning of the Giant Lord's incursions into smallfolk lands. After that, in Chapter 3 and beyond, true Giants can be encountered fighting with one another. Several Giant territories share borders and can be struggling with each other, such as Frost and Stone, Stone and Fire, Fire and Hill. Cloud Giants technically could be fighting anyone.
Making the Giants' war the central theme of the adventure
As written, the events of the town of Nightstone make little sense and leave too many unanswered questions. A better solution would be to make it the focal point of a battle between Hill Giants and Cloud Giants, both of which were after the titular Nightstone. This would be the first town that the PCs encounter in this way, and would foreshadow the later incursions
3. Turn the Giants into allyable factions
The Giant Lords are all obviously evil, by intending to increase their own power at the expense of everyone else. However, the players can play the Giants against each other, and possibly cause one to lead them to the Temple of the All-Father. It adds more interest to the game than Harshnag just randomly showing up, and puts meaning behind the puzzle to the Giants' portal.
4. Turn the Overworld into a Barbarian Wilderness
"Know, oh prince, that between
the years when the oceans drank Atlantis and the gleaming cities, and
the years of the rise of the Sons of Aryas, there was an Age undreamed of, when shining kingdoms lay spread across the world like blue mantles beneath the stars"
When the PC's meet Elves, they meet the Wild Elves of the Forest, who are uninterested in peaceful negotiations so much as they are interested in protecting the location of their forest homes. The humans that the PCs meet are Barbarian Tribesmen, following the territories and motivations listed in Chapter 3. Human settlements take inspiration from Viking and Gallic settlements of the early Medieval period. Orcs, Gnomes and Trolls need no adjusting to fit this theme.
The Dwarves are Scottish
Simply that. Taking inspiration from the Troll/Fyre-Slayers of Warhammer, the dwarves of Citadel Adbarr and Citadel Felbarr are vaguely Celtic Highlander proxies that love smithing. They also live in above-ground sod houses. Because Braveheart. They're also strongly allied with the Fire Giants, who taught them to smith.
5. Get rid of all references to other 5e campaigns
The Ring of Winter quest in Icewind Dale that goes nowhere and cannot be resolved without playing Tomb of Annihiliation. The Cult of the Howling Hatred. Blagothkus's Son. Klauth and the Cult of the Dragon. Just throw them all out.