Components of lacquer thinner vary somewhat depending on the manufacturer. Here is a list for a typical thinner: Toluene, Acetone, Isopropyl Alcohol, Methyl Ethyl Ketone, Propylene Glycol Methyl Ester Acetate. All of these chemicals burn just like gasoline, need less oxygen than gasoline, and have the same combustion products as gasoline. After combustion there is nothing left of the thinner that can do any more for the converter than the burned gasoline.
That goofy guy in the video makes up stuff, like what the thinner can do, and that the cat is still 95% efficient when the P0420 code is thrown. Always keep in mind that this is the internet, and people can make nonsense claims like those in the video and naive people will believe it and also pass it on to others.
Sure you can say try and see what happens. However, one gallon of lacquer thinner in 10 gallons of gas is a pretty strong concentration of a powerful solvent. I would worry about what might happen to any plastic or rubber parts in the fuel system.
Sorry, but those components you listed will NOT burn just like Gasoline. Does E-85 burn just like gas... NO. Does Gas with 10% Ethanol burn just like Gas?? NO. They all effect the exhaust gas significantly.
Sorry but the resultant gases from the thinner are going to change the output gas, one assumes that it is one of these gases, that cleans the cat. Also could be a temperature thing... if you raise the temp in the cat, it will burn off material that has accumulated in the honeycomb structure. My Semi Truck uses as similar principle to clean the diesel particulate filter. Injecting fuel into the honeycomb to raise the temp to over 1200F converting the soot to CO2. 2011 and new trucks take this even farther injecting aqueous urea solution after the DPF lowering Nox gasses to almost nothing.
Several other post have mentioned that a small drop in efficiency can cause this code to be thrown.. so it's not just this "goofy" guy that has claimed that. And someone else said this procedure worked for them in their Jeep.
Lastly I am FAR from Naive... I am just trying to help the OP to not spend Serious money on new cats, when he could try something else first. It's certainly his decision to make.. and it appears from his last post here that he has chosen to buy new cats.. fine. But at least he has made that decision knowing there ARE other possibilities.
As a long time car repair guy.. You NEVER start a repair buy simply replacing parts, unless you can VERIFY that the part is in fact bad. Or if the part happens to be inexpensive, and easy to replace. Or if it's the only way to diagnose the problem.
Anyway... good luck to the OP.. Hope you get it fixed.