To be honest, Sivir's Q does a ton of damage regardless.
Against a squishy her boomerang knocks out a good 1/5 of their life all game long. Against anything else, you're going to want the auto attacks for damage. Anyone with a bit of hp and mr or who knows how to dodge a skillshot is going to laugh at how low your damage is, even with the DFG.
AP Sivir works great if you're doing solo Q on SR and nobody else grabbed an AP or in ARAMs, but you don't have any sort of protection as solo bot in dominion. Sivir lacks CC and escapes, and her skillset promotes auto attacking. Stacking AP is inefficient at best.
PS. if you keep at it with the AP builds, at least throw in a Lich's Bane.
Would you like to play a game with me as AP Sivir because it is not inefficient. If it was I wouldn't be getting 2nd place wins as AP Sivir going bot when atm you get the least points going bot. AP sivir rules lols.