Just to report back...
I won my game with a tower victory (long, hard, and very frustarting when you get the "you can no longer continue building..." message and have to scour your empire for the node you just lost! But if it was easy, it wouldn't be a real victory, would it?).
Hyborem, who remained my faithful attack dog throughout the game, was in second place on points. I'd wiped out half the civs who'd stood in my way, and Hyborem obliterated one on his own for me. Besides myself and the demons, only the Calabim (amusingly cursing us for destroying the world, since they were fnow pious members of the Fellowship of Leaves) and the shattered, island-bound remnants of the Svartalfar (evicted from my home continent as I needed their mana nodes) remained.
Observations:
1) The Eater of Dreams is a one man army. I'd capture the highest population enemy city within reach, sacrifice as many of the population as possible and overrun surrounding cities with pit beasts. As these nasty creatures remain summoned all the while they win combats, they could rack up frightening city raider promotions. When distance or bad luck led to their loss, regroup and start again. Should I capture cities I didn't want, I'd just gift them to Hyborem after I'd wasted the locals (to be fair, sacrificed in his name!).
2) With a high Armageddon Counter, the number of demons rolling out of my planar gates was obscene. In the end I'd just leave them all where they appeared, as I just didn't need any more field troops.
3) A high Armageddon Counter is not entirely to the Sheaim's advantage, as I found when the Avatar of Wrath decided to waste my main outpost on the other continent, taking out both Abashi and my demon champion (Marmero?).
4) The biggest problem to counter in city management was poor health, due to a combination of Sacrifice the Weak, death mana and foundries (essential for the big builds). Even with all the health buildings it was a struggle.
5) My butchering ways led to numerous of my units going off to serve hell. Most of these I didn't care about (in presumably appropriate Sheaim fashion), but I was a bit miffed when Rosier disappeared. That vile-hearted monster was a killing machine.
All in all, I had a tricky start but luckily had good commerce and production from wineries and well placed hills. The power gain into the mid-game was slow but steady, fuelled greatly by a reasonably steady supply of Mobius witches, chaos maraduers, ritualists and conjurors, before achieving a critical mass that could withstand all but the most powerful of enemies (e.g. the aforementioned Avatar of Wrath).
Particularly fond memories were of obliterating Basium and his winged fools within about three turns of their spawning (unfortunately for them, right next to my principal overseas base), going on to annihilate the Amurites for daring to summon Basium against me, and after a painfully long wait (and with the game all but won), unleashing Meshabber of Dis to wreak fiery vengeance on those damnable Horsemen of the Apocalypse. I do the end-of-the-world stuff round here, alright horse boys!?
About an eighth of my home continent was hell terrain, the taint having crossed the ocean from the other of the two land masses, which was entirely an ash-shrouded wasteland.
Great fun, and all the more so foir the advice received here.