I read the whole thing. Not only is it incoherent rambling nonsense void of any scientific reasoning in a strange attempt to sell snake oil, it's very basic principle is invalid. Distilled water is NOT the same as deionized water. Not that deionized water is bad for a cooling system anyway...
My 2009 has Autel sensors and they programmed fine with the crappy 20 dollar amazon tool. Can't say how durable they are since I've only had them for 6 months. I'd stay away from Dorman, or any weird no name Chinese brand. Like Adsm said, try ford sensors first.
Well the fix is to find out the issue first. Need to get the actual codes (numbers). Autozone or places like that will do it free. Write down the numbers not what the guy says it means. A misfire dumps excess fuel into the exhaust, excess fuel burns up cats.
What are the codes? Cat's are probably fried but could also be red hot from excess fuel. Would be impossible for them to get that bad with no DTCs. If you don't fix the problem you will just ruin new cats if you replace them.