Does your new filter connect right up to the air meter? If so, then you shouldn't be having a problem. The only difference between that setup and the CTA is the stuff between the meter and the throttle body (it all goes away and is replaced with a pretty aluminum pipe). The filter fits right in. Why was your mech. looking at it? Was it running poorly? I don't understand. An airbox will allow even less air.
Maybe your meter was only saying that there wasn't enough. Did he check that?
