I dont think Robb necessarily would want the 7k but then again, he didn't really wanna be KITN either. Also, being a ruler of Riverlands means he's forever stuck defending its frankly impossible to protect borders from Lannisters, Tyrells, Baratheons if Stannis is Stannis and refuses to give up an inch and Dorne too if/when Daenerys/Fake Aegon attack.
He really doesn't have a choice but to keep on going. Also, he does want Sansa back. So he'd be journeying to King's Landing. He basically takes the Westerlands anyway (if you keep him conquering more and more and not returning for Hoster's funeral to be with Jeyne.) The Vale likely loses patience and joins soon enough especially if Robb tries poking the Vale Lords specifically instead of waiting on Lysa. So that's almost 4 of 7. Tywin won't defeat Robb in Westerlands.
Then take the Tyrells and Lannisters vs Robb. I think he could come up with some strategies there. Again, Tyrells won't give up chance to rule everything and Tywin won't ever bow down to peace.
So really it's not that Robb wants to, he literally can't stop until he makes it to the Iron Throne. Because no King will agree to the independence he wants unless he's the only King.
Robb's literally gonna be stuck because of his own success lol.
If you want Celia to be North/Winterfell focused. You could have her manipulate/talk her cousins/half siblings into going North and saving Winterfell alongside the Riverlords. Sort of that anon said, Robb's original supporters look North while Robb has to look South, going away from them more and more. This way Catelyn, his siblings when he gets them and sends them North will all see Celia and her daughter and bond with her.
Meanwhile Jeyne can have the newer Lords. I loved the idea that Jeyne isn't an Alicent type figure. We've had so many "mothers are emotional and make dumb choices" tropes in Alicent and Catelyn. Why repeat it with Jeyne and Celia.
Celia wanting to be home in Winterfell with Robb's family that's warm and happy is enough. She has fears but no ambition.
Jeyne is just happy to be with Robb. She's a healer herself. I think Robb might become desperate and dependent enough on her that he just brings an army of midwives and maesters along so Jeyne can travel with him. (Kind of another blow to Celia. Everyone seeing that Robb literally cannot be without Jeyne. Might help with some love potion rumours if you DO wanna try that angle)
Idk how Robb might help reduce the risk of crisis. He can't just...leave Jeyne. And I'm sure he'd think sleeping with Celia is a betrayal to Jeyne. And if he's gonna spend so much time with and in Jeyne, she's gonna be popping out kids.
Celia's daughter is his heir. Heck he might suggest the Rickon and Daughter marriage himself. He's not gonna be dumb and oblivious like Viserys. He's a King made in war. He definitely understands the threats and ambitions of others.
I'm not sure what he can do for Jeyne's sons. Except love them and raise them to be good and loyal to their sister. Idk?
Are you actually going for the "War of the Wolves" angle??? I'd legit go crazy waiting to read that hehe
All of this is very true, but I also think there are some members of House Lannister and House Tyrell that would be better willing to have independence of their own kingdom. Of course Robb would have to keep fighting to get rid of some of the members of those houses, such as Tywin. Without Tywin, a lot of things could and will fall apart. Robb would end Tyrion or, at least, dissolve his marriage to Sansa on the condition that Robb would support his claim to Casterly Rock and whatever royal title it could entail, should he wish to claim it.
And Genna Lannister is the wife of Celia’s older brother. The two are probably familiar with one another and Celia might be able to work things out with Genna about her sons (Celia’s nephews).
It’s all very complicated but, again, it all depends on how things develop as I write the more linear narrative.