Those are some bizarre symptoms

Right off the bat, though, I'd say to focus on that P0420 code. It never makes sense to run down one problem while the car's trying to tell you something, and I could see them being related.
I have a couple clarifying questions.
- When you say you have to push it uphill and you were bumping the RPMs to 4k, was the engine revving fine and you had a feeling like you were towing an anchor, or was it that the engine bogged down like the oil had turned to thick molasses and you were having to give it more throttle to maintain RPMs? It sounds like the latter, but I wanted to make sure.
- When you saw the driver's side exhaust glowing red, was the passenger's side glowing too?
- What sort of mileage are you getting?
- Any smoke after starting it?
In regards to the code, it's an indication that the passenger side catalytic converter is operating below threshold. Very, very occasionally just replacing the downstream passenger side sensor will remedy it, and some people have had luck with a sensor spacer, and others have had luck just filling up with premium instead of regular. I had 0420 and 0430 (driver and passenger cats) when I bought mine and ended up replacing both catalytic converters and both downstream sensors, which I think is the most common remedy.
My loose theory is that the passenger's side cat is plugged up and increased loads (like going uphill) exacerbate or amplify this problem. The engine not being able to kick the exhaust out properly would definitely explain an engine going maple syrup on you. I'm thinking it's like breathing through a straw: not a problem while watching TV or walking around, but it causes huge problems when you go for a jog.
It's not a cheap repair, so you'll probably want to search for P0420 on the forum so you can see what other people here have found and done. The part's a bit spendy ($3/400) and probably not something you can do yourself. I'm very inclined with a wrench, and am still glad that I let someone else do it. The bolts are inconveniently placed to say the least.
However, if replacing the cat(s) ends up fixing it, you likely have other problems which you should look into. Cats don't just go bad. On a well maintained engine, they should easily last as long as the vehicle. They generally fail because the engine is running rich, due to poor combustion (poor quality gasoline, too low of a grade) or things like leaky or stuck injectors, bad fuel pressure regulator, bad air/fuel/exhaust sensors, etc. You can burn that bridge when you get there, though.