Mathilde's recovery of the Karag Nar hoard means that bringing in income to Karak Eight Peaks is nice to have, but it's not important to the ability to consolidate and grow its holdings.
Belegar has probably already reached the point where the marginal value of extra money is basically zero, as he couldn't spend what he has now for many, many years, and that's assuming he can't get to the remaining major treasuries of old Karak Eight Peaks.
I think people are neglecting that the hold is still surrounded by countless enemies
I'd note that Umdungi leadership and increased Imperial trade would also incidentally generate the College Favor we'd need to rise to Wizard Lord over time, as we get Favor for Economic Benefit to the Empire.
The economic problem isn't income in coin, though it is useful.
The economic problem ultimately is that the Eight Peaks are
huge, and requires a huge occupation force to keep and expel the hostile, and that occupation force requires production to arm and feed them.
So take another look at Belegar's Stewardship options:
-Traditional Dwarf Industry - We'd see an initial surge in productivity as the Eight Peaks clans in exile move back in, and resume production...but what next? Dwarf industry produces lots of high quality product, but simply owing to attrition, they'd be low on the elders that produce goods valuable to other dwarfs.
--It will be done regardless, the clans in exile will return regardless, though the clanless moving in will taper off sooner without dedicated support.
-Mining - The motherlode is held by hostile parties, and is directly connected to a major Greenskin stronghold. Once they have it, they could buy whatever they want, but military assessment says it'd be bloody and costly in dwarf lives.
--It will be done regardless, far too many of our initial expedition were miners for it not to happen. That said, smelting equipment and expertise isn't cheap.
-Agriculture - Panoramia is doing her best, but theres a lot of harshly used land here...and it does feed a lot of settlers, this IS still a warzone. This will be an important supporting element regardless, but you need to get settlers coming in.
--The halflings will do this regardless, but they could finish the job sooner with more money.
-Trade - The big deal here is tapping into the Empire's trade networks. Long distance traders of luxury goods, Imperial raw materials, tools for the humans and halflings...and most of all, settlers. This is the fast-growth route, a secure trade route means that you can have settlers who don't need to sign up on a dwarf shipment to arrive, or brave the wilds.
--This part...we can't be very sure how it goes if we don't take leadership. The Umdungi could be anything, but we've just got a firsthand view from Roswita how thrusting an experienced adventurer into settlement leadership tends to go. Not many adventurers were former advisors to a king. Those who are tend to leave rather quickly in the night without telling anyone.
