Just used a minor variation on this deck (+2 SoG, +1 Lobotomizer, +1 pillar) with a number of upgrades (all creatures, 5 towers) to thrash Incarnate - accidentally starting a FG game on regular, not trainer
. Not an EM victory, because I killed him before I drew my second SoG. Gods without good healing and lots of momentum/poison and permanent control (Destiny, Incarnate, Neptune, Osiris if you get a Lobo out before dying, Paradox) can be taken down with that variation. Minor changes (with associated marks) allow you to take out specific gods - 4-6 steals for Elidnis, Fire Queen and Ferox; 4-6 protect artifacts for Seism; 2-3 purifies for Morte and Scorpio. It's a very versatile deck. Other gods can possibly be beaten with more extensive changes or more luck.
I haven't actually tried these btw, I've only beaten Osiris and Incarnate.
EDIT: So I switched to dark mark with +2 steal, +3 SoG, -1 Elite Immortal, and I've since beaten:
Divine Glory (got lucky, she didn't get a fire tower for ages, and when she did i stole it, so she only got two explosions in the game, and only had two miracles in hand - the rest of the hand I assume was explosions, so she was only drawing 1 per turn and then discarding)
Chaos Lord (well okay I didn't actually beat him, but I got him down to 10 hp - still with 2 steals in hand in case a dissipation field came up - but my shield chain got broken)
Destiny
Neptune
Morte
Seism (take that, bitch)
and Osiris and Incarnate again
Those were all without oracle foresight, so I'm pretty sure I could beat them with that knowledge. 2 steals isn't enough to beat Elidnis or Ferox unfortunately, especially not with 1 fewer immortals, and the damage is far too low to beat Miracle, so I removed her from the list. So I'm pretty confident my mostly upgraded variation can consistently beat 5 of the 24 false gods, but most of the others are impossible. Adding more cards slows the deck down too much and massively increases the chance of a break in your shield chain, which would lower the odds of beating those 5 and not give a big improvement against the others. In summary, don't use this deck to fight random gods, but fighting some from oracle is doable.