Like, the thing is that there appears to be literally nothing we can do to get Vragni to chill. That's the ultimate result of our choices, the consequences of pushing so boldly against everything he believes in. As a result, it would be immensely difficult and almost impossible to relax the feud between our two institutions. Any inroads we try to make openly will just infuriate Vragni further. Any subtle methods of relaxing the tension between our two groups of runesmiths will probably be countered by our counterpart once he notices them.
He hates us, he hates what we stand for, and most difficult of all, he wants as many runesmiths as possible to feel the same way. There isn't really a way around that. We've both made our beds and now the runesmithing culture of the far north will forever be shaped by it
True, but he's also an elder dwarf and shouldn't want a true schism any more than Snorri does. A public prodding might be a bad plan, but a private discussion could still make some progress.
Settling the whole thing would be ideal, but it's not really the only way to stabilize this situation. Coming to an understanding about the rules of engagement so to speak.
Our conflict doesn't have to be a friendly one, but stuff like making runesmiths of the other political inclination unwelcome in our areas of influence isn't necessary and risks starting something neither Snorri or Vragni can stop. We'd need to tread carefully to avoid making it sound like a personal insult, but they're both mature enough that they should be capable of frank conversation.
Given how old dwarves operate gathering some data and framing it in terms of a mutual problem and responsibility as elders would probably work. There are probably Snorrists being pricks out there too, so a data set pointing out problems on both sides and initiating the conversation on the basis of is being the responsibility of the one "instigating the point of contention" or something gives him some respect without actually acknowledging any fault or suggesting what we did was wrong.
Snorri did start this development after all, and as a runelord ensuring the guild doesn't tear itself apart is one of his responsibilities.
The key thing is to mitigate how clannish it gets, because dwarves go overboard with that. As long as we can keep the two groups feeling like they're arguing with their respected but incorrect fellows instead of a group distinct from their own this should stay stable.
That means both of them need to squash stuff like making other faction unwelcome in their spaces with extreme prejudice. Maybe even actively encourage ongoing discussion or collaboration if they can tolerate it. Making it popular to spend part of your journey deliberately seeking exposure to as much of the extant political spectrum as feasible would help a lot long term.