2000 Integra, P0420 code, new converter again??

I have a 2000 Acura Integra GS, automatic, with 65,235 miles.
One morning I started my car and heard a terrible rattling, took it to the shop to find that I needed a new catalytic converter. I replaced it with a universal fit converter, to save money. Great no more rattle! Two days later the engine check light came on and I contacted the shop that replaced my converter and they ran the P0420 code. The shop insisted that it was caused by the upstream oxygen sensor so I replaced that.
The code was cleared and I hoped that was the end of it.
After a drive on the freeway, engine check light on again! Back to the shop. To shut me up I got a new converter again, in case it was defective and the code was cleared. A day later the light is on again. Had another shop scan the code, same code of P0420 came up. I need to pass emissions to get tabs within 3 weeks. I am currently trying to get a waiver on emissions, this is really getting expensive.
As far as I know I have 2 options: Replace the converter with a direct fit, or replace the rear oxygen sensor.
I wonder if there is a specific code that goes with oxygen sensors, I have been told different things. Is there a way to test these components before replacing them?
Help me, please!

A faulty o2 sensor won;t cause a P0420. That code sets when the rear o2 sensor switches at the same rate as the front sensor. Abad sensor usually fails by being inactive(no switching). Some vehicles won;t tolerate a universal cat. You;ll probably need to get a direct fit.

When will it end! An 02 sensor will not cause a conveter failure code unless it's a chrylser product and the frt 02 is brand new and the rear is aging. Even then it's not common. Direct fit conveters fit in trash can the best! Buy a "good quality" or OE converter and have it installed and have the rest of the systems checked to see what may have caused the original conveter to break down!

To me, direct fit is the Walker Brand's OE equivalent. So, I would call a "Direct Fit" a quality converter, but that's debatable.
Good point COMP about the reason for the failure. Perhaps the converters were working and engine problems killed them?

I think I've seen enough "hatchet" converter install jobs to last a few lifetimes. I guess direct fit in my post should have been replaced with "universal fit" they 'll fit with a little welding and cutting and they'll be no gurantee that'll be the correct size for the application but we 'll make them fit. Sure it'll lower the pollutant level sometimes a bit but there's no gurantee they'll function efficently enough to do as well as the 0E stuff. I mean if most people knew what was in conveters and how costly those metals in there can be why would they ever think a 150 dollar one would work as well as a 500 dollar one?

I guess alot of people base their purchasing decisions on "cost" rather than "value".

It's definetly lack of training not lack of information

Ive had afew customers request the cheapest and even after a thorough explanation, they don;t want anything but the cheapest. I;ll put it on, but there;s no implied warranty.

I want to thank all of you for your input, it's been a great help. I will admit that I made my decision based on cost. Lesson learned the hard way.

It;s not your fault. Really, the technician should have advised you of that possibility.

assuming he is in fact a technician and not a muffler shop pipe hanger!