The key to your problem is the cat.Whenever you get all three readings high its ALWAYS the cat.Aftermarket cats only have to be warantied for 2 years,so the amount of precoius metal is reduced from oem[hence the price].Im not sure what burned out constitutes.If you melted the substrate then you have a really rich problem,but if your cat simply ran out of catylyst,thats fairly normal.I once ran a cavalier on a dyno with a pulled plug wire,and it passed,albeit with high hc and co.NOX was fine because the unburned fuel cooled the combustion chamberand the converter evaporated it.Converters do make a helluva difference.Next time you think you have a cat problem use a infrared non contact thermometer and measure inlet and outlet temp.If the difference isnt at least 50 degrees[usually more like 100] the cat is dead.Just remeber,when all three gases are high,its ALMOST ALWAYS the converter.As far as your lean condition,put an o2 sensor in,but I wouldnt sweat it if it didnt change anything.Also,if the engine uses oil[like often happens after a valve job on a high mileage engine]that oil coats the internals of the converter and it wont work for long.