I'll put my money on this.
More Information for STANDARD MOTOR PRODUCTS APS255
That P2135 is fairly specific, and I'm assuming it was the first code read. Plus the symptoms match what a defective one of these sensors would probably do.
It would be nice if just a new O2 sensor took care of the rest of the codes, but the P0420 is ominous. Sometimes the sensor takes care of that code, and sometimes it doesn't.