"She shouldn't be able to chunk from the range she's able to". And may I ask, why not? Let me point out that there are plenty of Champions who can "chunk" from range with just their basic abilities: Kog'Maw, Nidalee, Varus, Jayce, Twisted Fate, Xerath, Kai'Sa, Swain, Ziggs, just to name a few. And once again, this is just with basic abilities. The range on Zoe's Paddle Star only competes with theirs if she combines it with her ultimate. Add in the fact that to maximize her range she has to walk and Portal Jump in the direction of her target, and she puts herself in greater danger than other Champions who "chunk" from range.
"She shouldn't be able to stun from the range she's able to". The range of her Sleepy Trouble Bubble is remarkably short. The only way for her to increase it is by aiming through terrain. This means she's limited based on where the fight is happening, where her enemies are positioned, and she has to take positioning with these factors in mind. It's not like Lux, or Anivia, or Bard whose skill-shot crowd-control abilities naturally have greater range than Sleepy Trouble Bubble and can affect more than one target at a time.
"She can steal sums". Now this is just false. Zoe doesn't steal anything; she retrieves them. If you used Flash, and she picks up the Spell Shard, do you no longer have your Flash? Of course not. She didn't steal it from you. She just picked up a copy that you left on the ground.
I'm not saying you shouldn't ban Zoe, if that's what you want to do. It's just your reasoning seems a bit flawed.