Catalytic converters glowing red?

Could be. The coils on these vehicles have been known to fail. How long does it have to run before the converter starts glowing?

Sorry just posted this and then saw the videos. That thing is running pretty rough and that thing is red hot so you weren't exaggerating. I am surprised there are no codes.

However, now that I have seen that, your issue could be one of a couple things. First is a misfire so we need to suspect that coil.

Next, the converter could be clogged. Are you able to measure the back pressure? This is where you remove the o2 sensor and install a gauge made for this. If you don't have one don't buy one. Try removing the upstream o2 on that side and see if the engine smooths out. It is going to be loud but a clogged converter can glow and cause rough running. If you want to an exhaust shop can measure back pressure and it is pretty cheap. Cheaper then guessing at replacing the converter.

After that, we have to suspect internal engine issues as valve issues or piston ring issues.

Clearly with that glowing that red, it is a safety issue. That can catch the surrounding components on fire so be careful.

So it may be worth while to try and pull out the o2 sensors from that side and see if it improves. If it does then it is clogged.

If you make that change we clearly want to make sure the new converter and exhaust is not damaged. So if this is the issue then we need to find out why it was clogged because it will clog the new one as well. The most common thing that clogs converters is coolant and oil. So we will want to pressure test the system and maybe even test the cooling system for combustion gases.

https://www.2carpros.com/articles/head-gasket-blown-test

https://www.2carpros.com/articles/radiator-pressure-test

https://www.2carpros.com/articles/how-to-test-engine-compression

That sounds like the blockage is farther down then. An easy way to test if you have a welder is to drill a hole in between the items you want to test, Then use a piece of 3 16th brake tubing lightly sharpened to hammer into the hole. Then you just connect a pressure gauge to it. Start the engine and rev it a couple times while watching the gauge. You shouldn't see much over a pound of pressure if that. Then you pop the test tube out and weld the hole shut. For pre and post catalytic converter you can use the O2 sensors as ports, they use the same thread as a spark plug so adapters are easy to make.

You would be measuring the pressures in the exhaust system. An open unplugged system should have close to zero psi across the rpm range. A partially plugged system will show pressure that increases rapidly with RPM. A misfire will dump extra fuel into the exhaust and if the system is plugged that alone will cause misfires as the exhaust cannot get out of the engine and the new fuel doesn't burn very well. However a blockage past the converters is a real possibility. That location would let the extra fuel from the misfires get into the converter and ignite and it wouldn't mess up the O2 readings real bad as long as there was some flow. If there is a flange between the front converter and the rear you could split the exhaust there and see if it runs better. This entire thing could be nothing but a bad muffler or converter.

Not likely but the muffler could be rusted inside, or someplace farther up. Testing for pressure would show if it's the problem, and where.

The pressure testing uses nothing special, just a simple fuel pressure vacuum test gauge.
Not going to be the EGR. If it was open it would cause poor running but it wouldn't cause the converters to heat up like that.