It sounds to me like a fuel pressure problem, too. Could be the fuel pressure regulator or fuel check valve.
Just know that your engine and fuel injection is likely different than mbe32094's '94 E320.
If your car is a 1993 300E, then it has the same engine (either 3.2 liters or 2.8 liter M104).
If your 300E is a 1992 or older, then it is a different engine entirely (3.0 liter M103) with a different fuel injection and engine management system (M104's are HFM fully electronic ignition, M103's are CIS systems).
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".