My educated guess is that the timing chain has jumped a tooth and it is out of time. Had a 1969 Ford car that acted as you describe. At idle it would barely run, and when it was wound up it would run smoother. Incorrect timing will also cause your exhaust to runner hotter. If it did jump a tooth, I would not only replace the timing chain, but also check all sprockets, the tensioner, and chain guides. If it did jump a tooth, then likely there is wear elsewhere that would cause this to happen. Don't forget to check the crankshaft sprocket as well. I would replace the guides anyway if you replace the chain, as they are likely wore and are cheap.

I would think that it is not the catalytic convertor, as it would likely run better at idle with the lower exhaust output and worse when wound up with the increased flow. Had another car that acted that way when the muffler plugged up. You could try unbolting the exhaust pipe at the exhaust manifold and seeing if it solves the problem.

I agree with psfred, DON'T drive it that way, as it is a fire hazard and may further damage the engine.