A couple of important things. First, its true that lots of internet characters, including myself, are not technicians. But people like me get into doing cars because the technicians are so often wrong. Many of them are just blockheads with computer scanning devices and flow charts, but can’t think their way out of a paper bag. They also don’t drive my car everyday and know it like I do, nor do they give a rat’s tail about whether or not I end up paying for unneeded repairs.
Second, many people on this site are very good technicians and professional mechanics. Tester is one of them. But - and it will likely aggravate him when I say so - his telling of the tale of P04XX codes sounds just like what engineers write up about how things are supposed to work. And things do often work how they are supposed to - but sometimes not. Both that story and the dealer’s story about how the technicians would have found another problem if there was one puts way too much faith in the engine computer knowing what is going on. When I have a problem with a car I normally know it long before the computer decides to count it as a problem. And the computer can’t tell, for instance, whether upstream and downstream O2 sensor reading comparisons are out of spec b/c of the converter or because of something else.
Anyway, the easy point is that if your engine light now stays off then you needed a new catalytic converter. The above notwithstanding, it is the most likely remedy for the P0420.
The comment you got about gasoline from the dealer service rep is wrong if s/he specifically referred to high test. High test is just higher octane meaning it has a higher burning temp. The quality is not about octane (87, 89, 93). If you like you can search on “Top Tier” gasolines and stick to those brands. Also don’t overuse fuel system cleaners or any other kind of gasoline additive, and keep your PCV system clean.
Perhaps most important of all, you don’t need to take this vehicle to a dealer. Find a good reputable, local and independent mechanic. Some will specialize in Hondas. You’ll likely find bills such as this one cut in half. You can also ask them to have one of their techs look it over and get a second opinion as to why the cat failed. They all do eventually.