It seems you're trying to turn her into a scaling AOE/utility marksman, am I right in thinking that?
I can't help but feel that the current numbers will leave her on the weak side. She won't scale as well as Tristana (who even has some very good early game matchups to scale faster) or Jinx (who is quite safe while farming) for starters. Sivir now scales but has sacrificed any hope of winning any matchups in lane. A scaling champion who gets bullied is going to have a rough time. She also lacks the range of either of those champions so is far less safe throughout the entire game including when she's scaled up with items.
Sivir in general may run into issues with the identity you're pushing. On one hand her kit wants you to get into fights and kite (500 range, W bounce, E to block critical spells, R movespeed) but on the other hand she is going to be jumped on by people and get blown up. It feels like she may fall into the situation where she's rarely picked because a...