We don't know what exactly Morghur is. But his existence and presence is described in a way that makes it look almost like a spiritual force being incarnated upon the world and setting out to wreak havoc.
Furthermore, that "'just' reincarnates into some poor schmuck" and "has mondo chaos powers" is a very suspicious thing for a being to be doing or be described as. It's... I don't... hrm. Remember when BoneyM quoted people talking about Damsels and using multiple Winds of magic and said "In that case, put a lot of asterisks and question marks by the word 'human''? That, basically. Reincarnating like that? And having magical superpowers like that? That shit ain't normal.
Morghur's existence is partially spiritual in some way. Maybe he's like a Treeman, maybe he's like a Daemonhost, maybe he's like an Everchosen, maybe he's like a Daemon, maybe he's like a fucking ghost or solidified walking dhar or whatever the hell.
Regardless, I do think it's possible to bind him. If he's not a daemon, then he should be bindable the way Giants and Dragons are bindable with Kadon's skills.
If he is a Daemon, he should be bindable the way Dawi Zharr do daemon-binding. Or the way you get Daemonweapons.
Or he should be bindable as something in-between.
And then, throw in the Runes of Valaya to purify all the Dhar he wafts out, and you've got an explanation for why this place is not a writhing chunk of hell-space despite being host to Cor-Dum. And also why it's desertified, too. Things get transmuted by his aura, Dhar gets released, and then the Runemasters' art and workings burn away the Dhar.
I really like your thoughts on the Runes of Valaya, but I feel like you're going about it backward. If you were planning on purging Cor-Dum of Chaos, pitting your power directly against his is exactly the wrong way to go about it. Sure, maybe it'd work; the mountain waystones are absurdly powerful. But, then, so is he. Maybe you could overpower him, but it seems like, if you were planning on doing it, that wouldn't be something you could possibly be sure of ahead of time. Even if you succeeded in burning away all the Chaos, who's even to say that Cor-Dum would realistically survive it? I'm not very well-read on WHF lore in general, but everyone is treating Cor-Dum as though he's effectively Chaos incarnate. If you were planning on burning away all the Chaos in him, could you be certain ahead of time that it wouldn't just kill him temporarily again?
Instead, the theory I prefer is that somehow the dwarves and elves cooperated to replace the source of Cor-Dum's power. Rather than burn away the corruption after he starts spewing it, they're burning it away before it even gets to him. Instead of him treating the mountain like a herdstone after he'd been purified, it's integral to his purification because his power is being sourced through it in the first place. After all, that's what the mountain waystones are doing in the first place: they aren't pushing magic away, they're pulling in ambient magic and turning it into pure, dwarf-y power. If it was changed to do that in a bigger way, and they included a massive Rune of Valaya as part of the filtering system, then locked that in as the source of his power, it resolves the weirdness you'd get if you'd just bound him in a more standard way, and it sounds like a plan with fewer points of failure after it's put in place.
... One thing I'm less sure about is, does Morghur consciously or randomly warp everything in his vicinity?
We've been working on the assumption that his warping-field is indiscriminate and uncontrollable, from the wiki, but we have no idea if that's true or accurate in this quest. It could be that for the purposes of most observers in this quest's world, most people can't freaking tell if Morghur warps stuff on accident or on purpose or willingly or not, because all they see is the results. They don't see inside his head. Nor do they see him as what he's like when at a "home" so who knows.
Either way though... The fact that Borek didn't get warped and transmuted by Cor-Dum is...
I don't know.
Does it weigh things towards the "Probably bound somehow? Bound, and then Dwarfs are put on the FOF, so he physically can't Warp them" possibility? Or towards the "They somehow purged him of Dhar?" possibility?
Maybe Morghur reaching out and headpatting Borek was him trying to do the warping-and-changing on somebody, which he does with affection as he's essentially spreading a blessing. And then failing because the Dum Dwarfs naturally put Dwarfs on the whitelist to not ever be warped by him (or because Dum Dwarfs have other defenses against things or workings of Dum).
Or maybe he reached out and poked Borek because he's not an insane Dhar-tained monster anymore. Not sure.
This is the sort of weirdness I feel my theory resolves. He normally warps things around him indiscriminately and uncontrollably because he's normally effectively a conduit for pure Chaos, but he's not doing it now because the source of his power has been replaced. He's still throwing around all that power unintentionally, and visibly affecting reality, but because it's a different sort of power, it isn't going to hurt Borek. He's headpatting Borek because he's mainlining pure, Valaya-filtered, dwarf power, so he just loves dwarves as much as a conduit for pure dwarf-y power can. FoF targeting wouldn't even have to come into it.
"It is also hotter here than anywhere else in the Steppes."
+ "There is less ambient Dhar here than other parts of the Chaos Wastes Mathilde has seen, though still more than outside of it."
+ Mathilde's belt's rune: "Rune of Valaya's Vengeance: The third, the largest and most intricate of the three incorporates elements of both the Rune of the Furnace and the Rune that Valaya gave to the dwarves that allowed them to weather the coming of Chaos. It will grant you such resistance to flame that you could wade through lava, and burn off any taint of chaos before it could even touch you."
= "Maybe the Dwarfs did something with the Runes of Valaya to burn away all this Dhar? Possibly affecting Cor-Dum and the Beastmen in a positive fashion, possibly just making Morghur 'safer' to use or be around, not sure."
Yeah, basically. Just, I think instead of "burning it away," they're purifying it at the source, then using that to push the dhar back with ambient heat as an effect.