Stumbling start is most likely: Spark plugs, rotor, cap, wires, fuel pressure accumulator, or leaking injectors or vacuum/hoses under the air cleaner on top of the engine.
At high miles/age, pretty much all of that can use replacing.
As for the air injection pumps....I chopped the belt off of it on both of ours....
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-diesel is not just a fuel, its a way of life- 
'15 GLK250 Bluetec 118k - mine - (OC-123,800)
'17 Metris(VITO!) - 37k - wifes (OC-41k)
'09 Sprinter 3500 Winnebago View - 62k (OC - 67k)
'13 ML350 Bluetec - 95k - dad's (OC-98k)
'01 SL500 - 103k(km) - dad's (OC-110,000km)
'16 E400 4matic Sedan - 148k - Brothers (OC-155k)
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