Without an upped deck and/or plenty of shards, you have no chance at all against anything higher than Bronze (the big money-makers), and even Bronze may be problematic.
It depends on your rares, really. Limitless Speed doesn't need SoG, but they help if you decide to use the fatter versions. However, Limitless Speed also requires more upgrades to function than you may be willing to farm for. (You of course need to upgrade the key combo cards Light Dragon and Rage Elixirs, but you still won't win much without the Hourglasses and maybe Phase Shields upped.)
RoL/Hope needs both more upgrades and more rares than Limitless Speed, and doesn't win much more. Games are faster but more boring. Ditch it. At least Electrum Hourglass and Phase Shield are useful in other anti-FG decks; Ray of Light is useless for any grinder other than RoL/Hope itself, and the only other application of Electrocutor to FG killing is mono-Aether. Even then, Phase Shields could be applied to mono-Aether. Basically, the disadvantages outweigh the advantages of RoL/Hope.
Instosis is above all. But you need two more SoR for that, and playing Bronze Arena with an unupped deck can be more frustrating than playing False Gods with Liquid Antimatter.
There are other alternatives, of course. You hate Liquid Antimatter because it loses so much, obviously; it works significantly better if you're willing to shell out the cash on Tower Shields and Chaos Powers, though, so maybe you should try it in trainer. Still doesn't work well without a lot of upgrades, though.
I've never tried Flay 'Em myself, but I've read good things about it.
Throwing a few SoSac into almost anything makes it a better FG farmer.