Ah, Singed. No matter how many champs I fall in love with, Singed will always be my number 1. Check my profile to see I play ranked almost exclusively with Singed.
You asked about Singed's damage output late game, and I'm afraid that just isn't his late game role. His late game strength is, at it was already said above, the ability to dive into 5 enemy champs, grab the enemy champ who relies on their distance from the fight the most (ashe, twitch, kog'maw, any high damage ranged carry) and toss them where they do not want to be. Everything else is self explanatory, slowing enemies, gassing them, taking a ton of damage so everyone else doesn't have to, etc.
That isn't to say you can't stack damage if you want, but please believe me when I say that you are most effective, even if your goal is to kill, when you can take a severe beating. To this end I recommend the following to enhance your damage while still performing your role:
Rod of Ages
Rylai's Crystal Scepter
All of these items provide an increase to your ability damage while enhancing your survivability. I personally never get Abyssal but perhaps it will suit your aims. Good luck.