I have a lot of trouble with him, tho he could just counter my champions. He's too tanky to trade with, so he'll just push push push and after his first back, he can pretty much run right past your top tower and farm deep in your lane and you can't stop him. Top tower will get shoved, chasing Singed is a waste of time that makes you take heavy damage if not get you killed and you'll lose tower either way, and you're pretty much trapped top lane futilely trying to push the top lane back. Singed can leave whenever he wants to because he knows it'll take like 2 seconds to push the lane back up to your inner tower and that you can't stop him. And even if you and jungle do kill him, he doesn't really care and will go right back to being an nigh-unkillable pusher. And unless his whole team fed horribly, that game is probably already won right there, the tower advantage he gets off this is huge. Top lane will be absurdly pressured at all stages of the game and your team will be forced to deal with it and lose out on teamfights/objectives, not to mention the gold disadvantage.
I typically play Wukong, Riven and Renekton top. --- Funky Strong "Date vuelta. Veras el color rojo cuando termine contigo..." - Vega
I used to get soto against the ones who basically fed on purpose.
Imo that's not as bad but it sucks too because it pretty much locks you into top lane. The tower is always going to be shoved up to you, chasing Singed is a massive waste of time that nets you less gold than a minion if it doesn't kill you, so you get farmed as hell but you can't leave unless you want to instantly give up tower. I was Renekton last time this happened to me.
"Renekton, are you going to do anything but farm and kill Singed?"
"No promises." --- Funky Strong "Date vuelta. Veras el color rojo cuando termine contigo..." - Vega
Well, I think the problem is primarily your matchup. I think all three characters you mentioned will have problems trading with Singed. So I think the single fastest solution is to get a ranged/AP based champion.
Since you seem to be talking about "Proxy Singed" as well, then items that gives benefits when killing another champion is recommended. And this usually AP based items as well. --- Hope for the Best. But expect the worst.