Inspect for oil leaking from the engine valve covers. Oil on the exhaust manifolds or manifold flanges will get hot enough to burn off while under load of acceleration and hills/grades.
I have always accepted the rough idle of an ageing car as long as the air conditioning was comfortable. Rather than cutting the belt, you could have just turned off the A/C. I don’t believe the A/C clutch was harmed, it could have been damaged while it was operational if the clutch was slipping, shouldn’t make an odor if the A/C is switched off.