The light is on because the sensor behind the converter is not seeing enough change in the "cleanliness" of the exhaust. Basically, the sensor behind the converter is a tattle-tale. The computer sees the difference between the front sensor reading and the back sensor reading, and if it doesn't see a change, it throws the code saying the converter is bad.
I wouldn't replace the rear oxygen sensor. It sounds as if it is doing its job and reporting. There are DIY and HOW TO articles on how to clean an oxygen sensor, though I have never done so.
Options:
- replace the converter, though I expect the converter will fail again, dependant on oil burning. The 80.00 universal converter doesn't sound too bad, but you might consider setting things up so you can do it yourself down the road, when the replacement converter dies. How often it will have to be replaced at 80.00 per could affect decision.
- leave the converter, and watch performance and MPG to see if the converter is becoming clogged.
- gut or remove the converter, not totally legal, but you would ensure it is not becoming a restriction and causing further problems or hurting efficiency