Just had a thought.
It's way too late in the voting period for this and it's...
not the wisest idea even if it did work but I am curious,
@Boney what does Mathilde think about the prospect of revealing the belt and its ability to burn ambient Dhar to the Colleges and ask them for her permission to use Ulgu Tongs? It would never be something a wizard without the Belt could cast without going mad, but we would technically pass on the belt to another wizard after Mathilde's death which would permit the use them to use the theoretical mixed Lore(s).
Is this a 'you can ask but the answer might be no' request or a 'do not pass go, do not collect 500 dollars straight to the pyre' request from what Mathilde knows?