Mine had a similar problem and it was the fuel pressure relief valve.
It seems you're suggesting that your problem is fuel related, so the items to check would be: fuel filter, fuel pumps, fuel pressure regulator, etc.
I suppose without taking it to a mechanic and confirming that your problem is fuel supply related or possibly something else, the cheapest thing to replace would be the fuel filter.
I've replaced the fuel pressure regulator myself and it wasn't very expensive and is easy for DIY'er to replace.
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".