If I understand this correctly, you are currently employed by Company X. When you took the job with X they told you that any independent projects you work on have to pass through legal. You are now working on an independent project and legal is not giving you a quick reply??
The number 1 question i have for you is......Do you have a written employment/noncompete/ or any other written agreement with Company X???
Relying on "reasonable efforts" may not be sufficient as was earlier suggested. You really have to look at the express terms of your agreement, if any.
Without a written agreement i seriously doubt the enforceability of the noncompete. That being said, without a written agreement they can probably just fire you (without cause). However, in that event, i doubt they would have a colorable claim against your independent project.