The Juggernauts of Acheron
As technology advanced, one of the natural problems that denizens of the planes hoped to solve with it was the incessant worry of cube strikes on Acheron. A berk simply couldn't get a proper war on constantly worrying about whether a cube was going to crash into his camp -- or the battlefield -- any minute now.
The advance of materials science and the advent of crude rocketry made this a possibility. Armies with sufficient resources could attach engines to cubes and slow or even maneuver them relative to other cubes. With care, it was possible to pilot them close to each other and attach them, sometimes with struts (provides extra usable surface area that doesn't need to be hollowed out) or simply riveting two flat faces to each other (stronger joint).
The advantages of the setup were immediate. One no longer needed cubehopper spells to organize a multi-cube fiefdom, increasing warmaking ability. Moreover, a mass of cubes took less damage, proportionally, from strikes by lighter cubes. Maneuvering the cubes allowed one to move one's very fortress into enemy territory and launch a strike.
Size is advantage here; on Acheron, the bigger eats the smaller. If two cubestructs collide, the more massive is the safer, and will be likely to support more survivors to fight the ensuing battle. Outer cubes take the brunt of random cube impacts, leaving inner cubes sheltered and ready to carry on. The only advantage smaller cubestructs have is speed; engine emplacements can increase as the surface area of the cubestruct, while mass increases with volume, meaning an 8-cube assembly in 2x2x2 formation, for example, can project 4 cubesides worth of force to accelerate or decelerate (half its mass in cubesides), while a 3x3x3 cubestruct can project 9 cubesides of force which must move three times that many cubemasses. Naturally, incomplete cubes and amalgamations of different shapes have different structural and maneuvering advantages and disadvantages -- a planar arrangement of cubes has much less structural strength and no protected inside but can bring a 1-to-1 ratio of cubesides to masses in accelerating and decelerating.
Eventually, the great empires of the plane -- the orcs, the goblins, and a power or two that cared for such things -- have amassed enormous cubestructs. These enormous complexes flare with engines on the outside slowly propelling and maneuvering them, while the inner cubes sit in the protective shadow of the outer ones. Single cube-islands, faster and more maneuverable (though of course still enormous and clunky compared to personal vehicles), are sent out with raiding parties. The local space around them has been relatively cleared of random cubes, though there is a constant inflow from the (infinite) unconquered regions of the plane.
This strip-mining keeps the cubestructs safe, but it means that convenient building materials are now hard to find. Raw cubes must also be hollowed out and engines attached, a slow and expensive process. It's much easier, then... so to speak... to take over a large cubestruct fortress already arranged and outfitted. Thus, the wars rage on.
This idea is mostly for Avalas. Tentative ideas for the other layers:
Thuldanin: the stone to which visitors turn is now silicon, shot through with copper. They aren't dead, so they can't be resurrected, and they're not petrified, so they can't be unpretrified... They're trapped in the collective hivemind the plane became when too many computerized weapons came here, froze, and were twisted by the energies of the plane into a malevolent intelligence that could sense and operate its mechanical junk. The entire plane is now an entity with a single purpose: collect visitors long enough to assimilate them, and use its awareness of still-useful weapons to deal arms across the planes, fomenting wars to keep itself supplied and powerful.
Tintibulus: nothing at the moment.
Ocanthus: no ideas presently.
In principle, I like this one, and even one layer (or, for that matter, a layer and a half) is a good start. The cube structure thing is a shade technical; it'd need streamlining to be playable, but it certainly works in theory.
And I think I'd probably like to see a bit more of where you're going with this (or others' ideas, for that matter) before going into more specifics or depth.