At 145 games in for 1.22, here's what it's looking like thus far, using PuppyChow's original deck...
Overall:
22 EMs+34 wins = 56 wins=38.62%
7 DOs+82 losses = 89 losses=61.38%
DOs (deckouts) were caused either because the Eternity was the last card in the deck, Eternity was destroyed by the FG (even when I played it as late as possible), or I ran out of time quanta. I begin conserving time quanta (not using hourglass or abilities) as soon as I have control of the board, or by when I have 12 cards left, whichever comes first... For some gods, I conserve the steal specifically for a time quanta to help build up a pool early on as well. 7 DOs across 145 games represents a 4.83% chance of DO due to various reasons above. The standard expected rate for DOs assuming you go through all your cards is 2.94% (1/34 cards), so in addition to the time quantum shortage and the possibility of having the Eternity either stolen or destroyed, it seems about right... A rewind or second eternity may reduce this issue, however it would also require even earlier conservation of quanta in order to play the cards... would be interesting to test, but 4.83% seems pretty low, and I expect the number to continue to decrease as I play more games. As for the FGs:
Chaos Lord (4-1) 80%
Dark Matter (0-6) 0%
Decay (0-7) 0%
Destiny (3-1) 75%
Divine Glory (0-5) 0%
Dream Catcher (3-4) 43%
Elidnis (3-3) 50%
Eternal Phoenix(0-7) 0%
Ferox (2-3) 40%
Fire Queen (2-3) 40%
Gemini (0-1) 0%
Graviton (3-5) 38%
Hermes (2-3) 40%
Incarnate (7-3) 70%
Miracle (2-3) 40%
Morte (5-5) 50%
Neptune (4-2) 67%
Obliterator (1-8) 11%
Octane (3-3) 50%
Osiris (6-6) 50%
Paradox (3-1) 75%
Rainbow (0-5) 0%
Scorpio (3-1) 75%
Seism (0-3) 0%
Still plenty of testing that needs to be done, but between my stats and some of the other's that have posted, I'm getting a pretty good feel of which FGs you can dominate and which ones you can't. I'll continue to play until I can have at least 10 games per each FG (240 games) to see what the numbers look like then.