From what you describe, I'd go with chaotic neutral.

Chaotic neutral characters can have all kinds of reasoning and motivation. Chaotic ethos doesn't necessarily mean the character is insane, criminal, completely random. My most recent character was chaotic, but she was neither insane nor random, and she never broke the law. She was, however, whimsical, quirky, and took unpredictable approaches various situations - ergo, chaotic.

Basically the consensus is that it is outcome that determines ethos/alignment, not motivation. An evil character might think his actions are holy and good, but ultimately, if his actions are evil, he is evil. This is a discussion we've had before. Similarly, if a character thinks he is reasoned but his actions are random by all outwards appearances, I'd say that it qualifies as chaotic.

That said, it's highly improbable anyone is going to nitpick whether your character has a neutral or chaotic ethos. It's rarely that important of a distinction.