The first time I read your post I thought too much fuel was causing the
glowing exhaust. But the the sputtering as you describe it led me to the
fuel starvation theory.

Does the exhaust smoke black? Does it reek of unburned fuel? If so, the
motor is being over fueled. If not, I stick to the fuel starvation
theory which causes misfiring and that unburned / partially combusted
mixture is burning inside the exhaust and so causing the exhaust to
overheat.

Another thought is that the catalytic converter has disintegrated and
the exhaust itself is obstructed and that's causing the motor to stumble
on any occasion where you demand some power.

I repeat, check the fuel filter to ensure the motor is adequately
fueled, if only to rule out the fuel starvation possibility.

Tom is right.

Too lean mixture will overheat the catalytic converter.

I had a similar problem with my 1991 300SEL (W140, 104 engine). My
problem was a defective air mass sensor, but anything causing too lean
mixture would cause the a similar problem.

In my case, the symptoms were exactly as you desribe. The overheating
caused the catalytic converter to burn out, clogging the rest of the
exhaust system. So the engine had two problems: Lean mixture and
clogged exhaust. Before clogging the exhaust, it would run reasonable
when cold (due to richer mixture) but with limited power when hot. With
clogged exhaust it was almost no power.

Be careful. A burned catalytic converter (probably already happende
according to the policeman) is expensive.