If you want the fastest ttw you have to think hard ^^.
example: it is turn 3. and you have 5 quanta. If you suspect to win in 3 turns (ttw 5) you play an elite charger for 21 damage in 3 turns (avg 7). if you suspect to win in 4 turns (ttw 6) you play an overdrive for 30 damage in 4 turns (avg 7,5)
so you should only play overdrive when you suspect the match will take 4 turns (and no more, than the creature dies) to win OR when you don't have an charger in your hand.
hmm, if you don't want to think to much it is the best option to play chargers first, then overdrive, then gravitons. that 2 damage gain when 4 turns left isn't important. (and overkill means that if the creature dies you lose 2 cards).
I suspect that longsword is better than Gavel. for 1 quanta you can get more than 1 damage in this deck.