Since your car is a later 240d it does not have the vaccum pump that feeds to the intake. If oil gets through the internal diaphram seal it would cause a simular condition as yours. The output line from the vacuum pump then also is wet with engine oil inside.

This is unless someone put an earlier engine in the car. Follow the lines from the vaccum pump. Make sure they have no apparent oil inside. Your vaccum pump is still shutting off the car so you would not have a total diaphram failure. If it was total the engine might really get going and car would not turn off with the key.

You might also install a temporary additional spring to the linkage just to eliminate a linkage that has not closed down. I know when this speed up is occuring you are too busy trying to get the engine shut down to examine the linkage. First just make sure it is not the earlier engine.