I believe a lot of the campaign problems Beastmen, Greenskins, and Wood Elves face could be alleviated with a new type of settlement.
Deep Forest regions (or Wild Woods, Dark Forests, or Untamed Forests) are places across the world where grand and wild forests grow, their canopies blotting out the sun. Although people often live here, civilization seldom flourishes. All manner of feral, wild, and darksome things thrive in these shadowed woodlands.
Deep Forests would be a preferred biome of Wood Elves, Beastmen, Greenskins, and Vampire Counts. They would be unpleasant for everyone else, but like the Chaos Wastes, they provide different building options and constraints based on how the occupying race perceives the territory.
Most importantly, Beastmen can actually build settlements in Deep Forests. They would only have limited recruitment capacity from the places; they would still be first and foremost a horde faction, but Deep Forests would be safe havens. They could build shrines, herd-stones, and defiled menhirs that provide heavy garrisons, corruption, and background income. Claiming a Deep Forest location would give them a sort of forward base where their raiding stacks can fall back, regroup, and from which their Legendary Lords can respawn. This should turn them into more of a constant threat rather than a flash in the pan; defeating the Beastmen would be less about wiping a coupe marauding hordes, and more about rooting out their heavily fortified holdfasts in the heart of corrupted wilds.
Wood Elves would also be able to build meaningful settlements in Deep Forests. They could have improved versions of their normal outposts, but also the ability to upgrade the settlement. Critically, they could build structures that link the Deep Forest settlement to Athel Loren, through the World Roots, allowing fast travel between this forest and their sacred magical forest. Again, this would turn Deep Forests into valuable, forward bases for the Wood Elves, while Athel Loren remains their primary base of power.
Vampire Counts and Greenskins could use Deep Forests as minor holdfasts. Greenskins would gain access to a bunch of goblin-themed buildings and Vampires would find haunted barrows or ancient battlegrounds that would let them recruit a lot of low-tier units. Both of these races find the territories easier to occupy, hold, and fortify than human factions.
The Old and New Worlds have a lot of places on the map that are mostly empty save for hard-to-travel forests. Much like the Massif Orcal, Deep Forest settlements would consolidate these areas into small territories, either adding them to the larger provinces or making them single-settlement provinces. (There are some interesting implications for both approaches).
There are a lot of good locations for these:
Laurelorn Forest: in the northern Empire, mostly in Nordland, where Morghur starts.
Drakwald Forest: in the western Empire, mostly in Middenland
The Great Forest: in the north-eastern Empire, mostly in Talebecland and Ostermark
The Forest of Arden: already a province in Brettonia
The Sombra Wood: in central Estalia, where Khazrak starts.
Forest of Gloom: in the eastern Border Princes, just south of Blackfire Pass
Hvagir Forest: in the western Border Princes, just south of Karak Izor and the pass into the Vaults
Albion: just the entire island
The Black Forests: in the Clawed Coast, in Naggaroth
The Doom Glades: in the titular Doom Glades in southern Naggaroth
The Deadwood: in the titular Deadwood, in northern Naggaroth
A neat idea that came up from the original thread was to make settlements in Deep Forests hidden, similar to the Skaven mechanic. Deep Forests not occupied by civilized societies would just appear wild on the over-map, and would need to be investigated to determine who owns them or what may be lurking there.