I think we should definitely include Gondor in this story. I'm not as keen on using the 'commando' storyline, but I think it could be made to work.
The scene I *want* is for Gandalf to visit the court of Minas Tirith. The reason for his visit is definitely connected with Sauron declaring himself openly, but he is going to try to lay out what he thinks the risk from Harad is: a very populous region is being courted by agents of Sauron - a region with both historic ties to Mordor and a history of being an enemy of Gondor. What will Gandalf urge them to do about this? Not go to war with their neighbor to the south! He'd only suggest that if he is convinced his mission has failed, or if someone in Harad is openly campaigning for war with Gondor right now. Would he, rather, urge them to make peace with their human neighbors, before Sauron takes hold of the land? That would be considered quite radical (and not necessarily welcome) news in Gondor.
The court of Gondor contains all the characters we need. Recall that we are 70 years before the War of the Ring (TA 2951). The agéd steward is Ecthelion's father Turgon - he's 96, and he'll be dead in a couple years. He is unlikely to go along with any radical suggestions from Gandalf, but also unlikely to provoke a war at this point of his reign (sending 'commandos' would not be his idea!). Ecthelion is probably likely functioning as steward already - he is 65, and as one of the Dunedain, likely looks younger than his years. One of Ecthelion's policies will be to invite young men from outside Gondor to enter his service. Now, Thengel of Rohan, who took service with Turgon, could be the impetus for this policy. But it could also be something that Gandalf says now that will set that in motion. [If we don't include that in this frame, it can definitely be part of the 'Thorongil' frame - perhaps the Dunedain from the north meets a young man of Harad in Ecthelion's court, and is inspired to travel south himself (we know Aragorn does this!)] Thengel is only 46 years old, but he's also from a shorter-lived family (he will live to 75, not 98 like Ecthelion). The fathers of Ecthelion and Thengel will both die 2 years from now, leaving them as official rulers at the same time. Currently, Thengel lives in Lossanach with his wife and two young children: Théoden is a three-year-old; he has one older sister. Ecthelion has 2 daughters, and of course his son Denethor is an unmarried young man of 21.
So, this allows for a lot of potential different reactions to Gandalf's news and proposals. Gandalf is all about kindling minds and hearts, and he is the enemy of Sauron. So, his goal is to unite people against Sauron, not allow them to fight amongst themselves. He *has* to be urging a peaceful, diplomatic action here, right? But the reality is that...people do fight. Perhaps Gandalf is seeking military aid for the beleaguered underdogs who have not yet fallen to Sauron's sway in Harad? If they knew they had the support of Gondor, would that change their situation or how isolated they feel?
Thengel moved to Gondor because he famously did not get along with his father. And he's content to stay there until his father dies. When there is that sort of fighting within the family, the idea of making friendships with a different people more commonly seen as 'the enemy' is difficult to swallow. On the other hand...he has been a 'foreigner' living in Gondor, and he might have some perspective on what it is to be different and yet accepted, and understand exactly what Gondor can offer these folks in Harad.
Turgon is 96, dying at 98. It is difficult for me to believe that he's much interested in what is happening outside Gondor's borders right now. He's had a very peaceful rule. I would be comfortable painting him as an insular leader, focused on the safety and prosperity of Gondor, and not much worried about what is happening in Harad. And no, it's not just because he's elderly - his name is Turgon, so we should definitely lean into Aredhel's complaints about her brother.
Ecthelion, on the other hand, will prove during his own time of leadership that he is interested in diplomatic outreach towards other lands. I would love for him to invite 'this young man of Harad Gandalf speaks so highly of' to visit the court of Minas Tirith.
Denethor is going to grow to distrust Gandalf over the years. Might as well start now. What is Gandalf doing, consorting with the enemies of Gondor, and then trying to persuade the aging steward to accept them and go 'soft' on them? That is how Minas Tirith falls! Denethor can see through his pretty words, and recognizes what Gandalf is attempting to do - he wants no part of it. Too bad his grandfather is all 'I remember when you learned how to talk' and ignores his warnings/advice.
I see the 'Gandalf goes to Minas Tirith' as a one to two episode break in the frame, so that time can pass in Harad while he is gone - allowing the situation he walks back into to have progressed. Gandalf has to have a reason to go, so he is trying to get help of some sort for the Haradrim. Whether or not he manages to win over anyone in Minas Tirith is an open question, and whether or not the 'help' he brings is welcome in Harad is another question.
If the 'commandos' happen, it would be because Gondor refused Gandalf aid, but decided the threat in Harad was real enough. Denethor is the right age to be with this group, but I doubt Ecthelion would send his only son on this mission to Harad.