What APC (bot lane adc alternative) benefits the most?

I don't plan on using this unless absolutely viable and necessary, but I've been thinking about how some AP champions can get past a bit of their early game weakness by having a support, or even some AP champions being very powerful in 2v2 situations verse an ADC and support.

So, assuming there is some marksman on my team (most likely top lane vayne, graves, draven, etc), which APC can work most effectively in the bot lane? I would assume item reliant champions like Swayne or Vladamir, but Vlad is also level reliant, making him a poor choice. So I'm basically left thinking maybe Azir or Heimerdinger for bot lane dominance, Karthus to bypass his weak early dueling potential and push him into his absurdly strong lategame by being fed all the money, and Lulu for basically being capable of being a support carry. She is a fairly safe carry and her abilities scale so well off of ap and items that she might be the best support carry.

Any thoughts? Please don't claim I'm an idiot or anything, I put a lot of emphasis on counterpicking and building great team comps. I would only do this if I wanted to fill a huge hole in the team. EX: Master Yi jungle, Vayne top lane, Zed mid lane would leave the team with no CC or AP. Going an APC or support carry might be better than an ADC, assuming I am able to handle the enemy bot lane, which I would always consider.