Mid laners like Ahri

Would like some tips please - mid laners like Ahri. After a bunch of games top or bot where the enemy mid laner camps me and ruins my game (followed by my mid laner doing nothing and complaining that I'm feeding his opponent...) I decided to go back to playing mid. Given that I'm winning a lot more despite not playing it for so long, I feel like it's where I should be playing.

Problem is the only mid champion I play right now is Ahri. I've only ever really played Ahri mid (dating back to pre-dynamic queue where I only went mid if Ahri was still available, and post-dynamic I never queued for mid).

So I want some suggestions on who else to pick up. Most similar to Ahri would be great as it would help the learning curve. My criteria:

• AP champions only, I will not be playing an AD mid laner (I just really dislike them, I feel like the mid laner is the team's consistent source of magic damage
• Strong throughout the game (i.e. not someone who falls off late, and not someone who's really weak and becomes a hyper carry). I don't mind being weak pre-6. Just want to be able to exert influence on the map before the team falls too far behind and not feel useless late.
• Preferably a decent roaming champion, or otherwise a way to exert map pressure.
• Preferably somewhat mobile without flash
• Preferably some form of CC

Basically, a jack-of-all-trades master-of-none sort of deal (Ahri's identity).

Some ideas I have had: Karthus - only sacrifices mobility. Ultimate is great map pressure - strong post-6. Lissandra - she would double as an AP top lane pick up that I should probably be adding for when my mid laners are AD. Seems to have all of the above requirements. Diana - Seems to satisfy most, and she's always my biggest problem when playing Ahri (so she'd be good to learn to play against Ahri, and playing her may help me learn to play against her). Karma - Satisfies most requirements as well. Lulu - IDK why, I just feel like she may be appropriate.

Any other suggestions?