I can see how the game could work like W:I:
The kingdom could be represented by the headquarters of each army on the planet, as well as the fleet orbiting the planet.
The quest zone by a battle orders area where orders are issued to squads who gain bonuses based on completing objectives (like say assassinate an hq unit or destroy three vehicles).
The battlefield could be represented by basically the rest of the planet the armies are fighting over, with maybe different terrains that effect which troops can fight (land, air, heavy, light infanty...etc, ).
As well as a fourth zone could be added representing space where ships could fight for orbital dominance and maybe certain ships that can take potshots at the rest of the zones (with surface to orbit weapons systems to fire back).
one of my ideas could be instead of fighting just over the zones; the battlefield could have special cards that determine what types of units can fight in it, because in W40k you don't fight over just one battlefield: you fight for the entire planet! examples of such could be: forest zones, cityscape, mountain regions, snowscape, grasslands...etc
On the solo area I think it is possible: you could run it like the LOTR LCG where you fight a deck based on battle orders; using the one of the other decks you would get in the core set it is possible to fight another army if there were cards that dictated what is played into the ai zones, maybe instead of the draft cards like from the core set, you could get a solo deck that is drawn once a turn which says what is done by the enemy ai like in the gears of war game.
That is all the ideas I have for now, but if anybody wants (FFG! ;P ) I could try to draft up a basic rules set and maybe an example game.