I'm may be going out on a limb here. Pro techs correct me if I'm wrong.
The fuel pump relay on the 88-89 300SEL's in setup pretty much like the 300E W124 with the 103 motor - fuel pump relay somewhere near the battery. Don't recall the acronym or name of the gadget it lives behind, but it's in this general vicinity - much has been said about it here - check archives.
I'm not saying that tapping the fuel pump didn't help, but on the 88-89 300SEL's, the fuel pump relay is notorious for causing the sort of problem posted.
I wonder if there was enough of a cooling off period and tapping the fuel pump was merely a coincidence?