Good for you! I have a 4AFE equipped Corolla and have been battling the same problem, high HC’s making it not pass Calif emissions. There’s a thread you can probably find using the search feature here on all that, if you run into this problem again. I can always get mine to pass, but barely. A combination of retarding the ignition timing, making sure the engine is properly heated to operating temp, new spark plugs, cap, rotor, & wires usually does the trick. Sometimes I have to use an injector cleaner too.
I expect my problem is different than yours, since you had a brand new cat. My cat is the same age as the car, 24 years. But your post makes me wonder if I might have a little bit of a fuel pressure problem, so I’ll check that out next time emissions testing is up.
Edit: One thing that seems to help for HC is to use the type of NGK plug called “V-Groove” , or something to that effect. Yields a little bit more robust spark I guess.