Imo, the best way to rework Kalista is to make her the League's first official AD support. It fits her theme as someone who helps attain vengeance, one way or another. It fits her kit's decent poke, free vision ghosts, combo with soulbound damage, her slow and her get-out-of-jail-free ultimate that takes her carry out of just about anything, or makes for epic chases/engages.
Only a few tweaks would be needed; Make the W combo damage proc for her ally and not herself so Kalista can't gain kills from it's procs, have her W's bonus AS for being close to an ally apply to said ally, and lastly, make her Ultimate grant a shield of moderate power upon coming out of it to promote engages/help escapes.
The only issue left then would be items, and i'm not the only one around who'd dream of AD support items being put out there. I say; if we add AD supps to the game, take all on-hit effects that either debilitate or otherwise hinder enemies and make it into the AD supp's stuff. They'd have a niche of their own then.