I believe it takes several ignition cycles to reset the on-board computer rather than miles driven. How many? Not sure.
Do you know what the actual code is? Did you fail inspection because the Catalytic converter failed or because you had the Check Engine light on? If you have the code, post it. You can try Sea Foam but I doubt it will work but no harm in trying.
Anytime the “check engine” light is on, try to get the code rather than the diagnosis. As you can see, you got 2 different opinions. whereas with the code, there is a diagnostic procedure to follow and many Quest owners may have already dealt with the problem and are able to assist.
Many auto part stores will scan your computer for free.