[acammer]

The little backfire sounds like it might just be the typical deceleration sounds you'd expect to be heightened with a louder exhaust. Same with the imperfections in the idle - a stock exhaust will mask those but a aftermarket exhaust will let you hear more of that.

If the exhaust was plugged somewhere the problem would worsen with load/rpm. If it pulls strongly through first gear to the red-line with your foot to the wood then I don't suspect it's a plugged exhaust. If the shipping plug was still in place then you'd have a hard time getting rpm out of the car even under light load - and things would sound pretty weird.

Is the exhaust clamped or welded in? If you're convinced the cat-back did then, and it's clamped in, then loosen the clamps and drop the exhaust - just tie it up for a test drive, and validate the condition is gone or persists. (It's gonna be LOUD!) It's hard to imagine a catback causing such trouble. You should be able to run open-header after the rear cats without a problem, so the freer flowing isn't a concern, just a potential blockage.