From memory and since I see it so many times the P0420 is “Catalyst efficiency below threshold” correct me if I am wrong.
Most common causes? A leak in the exhaust system and or bad O2 sensors. However coupled with the temp sensor issue you may or may not be having… it can relate to the 420 code. If the engine thinks its cold all the time it will enrich the fuel mixture…which will coat the O2 sensors as well as the catalyst matrix with excess soot…which will cause all sorts of problems that basically snowball. The Cat wouldn’t be able to properly scrub the exhaust of Nox emissions if it was heavily coated with soot. You mentioned how your old O2 sensors were heavily sooty with deposits. Well that same soot would also in the cat as well. Cats rarely go bad, but everything has its limit.
If the engine cannot measure its temp accurately you could be running very rich all the time. Is your fuel mileage very poor? Do you have any exhaust leaks?
First order of business is to suss out the temp issues you may or may not be having and also be sure you have no exhaust leaks. The engine computer cannot adjust the fuel mix correctly as long as temp or exhaust leaking is a possible problem and that is pretty important. After you sort out any temp/ exhaust issues then you can move toward the 420 and other sensors/Cat/exhaust issues.