A P0420 just means the cat isn't working to its expected efficacy. There is a O2 sensor before and after the cat, the PCM compares the readings of the two sensors and makes sure the cat is working properly. As far as the surge problem it'* really hard to diagnose a drivability problem such as this without a scanner that reads live data. Right off hand most surge issues are caused by a bad mass air flow sensor but you say all the sensors have been replaced. It could be a vacuum leak around the intake. Just my inshallah thoughts.
04 Yukon XL 2500 4x4 8.1
91 K-1500 5.7 RV cam 700-R4 stage 2 shift kit
08 Cadillac SRX 3.6 AWD box stock
49 *****'* CJ3A Jeep
There is no replacement for displacement!