tl;dr: You've got all the internal parts down; I think you're worried about the silly because you're just not certain yet what image you (and he) want(s) to project. Getting to play Superman more as well as reporter!Clark might help. Now go tell me what I'm doing wrong.

H'okie, the long version: From experience, playing the nice (or not constantly angst-ridden) ones <i>is</i> hard. You're making him proactive, though, which is usually where people fail.

You've got his core qualities--the mind behind both Superman and the reporter--down pat. I <i>love</i> that you're actually using his love of journalism, and how you use 'Clark' and 'Kal' in narration. They give another layer of context to how he's thinking of himself (and his relative humanity) and perceiving the world at any given moment. The rest is cosmetics. He does feel adult to me--playful, but that's a good thing, and definitely part of him. As to your 'silly' concern (stream-of-consciousness beware):

You pulled Clark from a canon point with distinctly Reeve-esque mannerisms in both writing and drawing, and I think that's shaping some of your play and why you have a 'too silly' feel. Geoff Johns wrote a post-Crisis interpretation with some Silver Age-flavored mannerisms. It's especially true with the public Clark Kent persona (the 'silly'). On average the post-Crisis reporter-Clark seems to retain real!Clark/Kal's sardonic and confident demeanor, but with a self-effacing approach to 'mild' to contrast against Superman's overt force of personality. On the other hand, the turtle's a totally new situation. It makes a lot of sense that Clark would fall back on some silly until he really got his bearings, and then slip into a more natural rhythm.

I will add that I think you may be overcompensating somewhat because you haven't had as much opportunity to play Superman rather than reporter!Clark. I think you'll find the line more easily once you do. There have been so many equally canonical characterizations that, at the end of the day, it's your call which you feel most comfortable with.

The big thing I'd say to watch out for: sometimes his word choices are more patronizing than I expect. Content-wise, sometimes he just is, and you're good at that. It's just idiom.