I've got few thoughts to share with you guys. I hope it will help with choosing right direction for Ahri.
-Movement speed on Q feels very important for her. Without it she feels very slow and clunky. I suggest not to remove it, just adjust so she will get less.
-Version one felt like an assassyn. She could burts someone and she was usefull even when R was on cooldown.
-Version two felt strange. She was on the weak side of dealing damage. Also she was useful only in extended fights. Then when R was on CD she was useless. Reduced cooldown on spells was kind of nice but not super good.
I think about something between these two. I would love to test these changes. Might be very unbalanced at 1st but hey, if we want to find right direction, we need to change something to extreme just to find out where is the edge.
-Q half as much movement speed as right now
-W and R, every missle that hit's different champion will reduce cooldown on Q by a second
-E less damage by itself but 20% damage amp for 6 seconds only for Ahri
-R ammo system like Akali have. So Ahri will have only 2 jumps but everytime she wants. She gonna get one every 30sec and every kill/assist she will get two back.
I really would like to try this one.