I recently has the EXACT same issues.

I have a 1993 500E that would start fine and run awesome. But after 5 minutes it would stumble but continue to run as if on half an engine. And if I stopped on a hill... Forget it! I would not be able to pull away from the curb because the car had no power to get it moving.

And with a 500E that's horrible as it's programmed to start in 2nd gear. And San Francisco is not short of hills.

After much anguish my mechanic hooked up a pressure gauge and drove it. He found that the pressure dropped after a few minutes of driving.

Replaced the fuel pump and filter and I'm "lighting up" the rear tires again.

You mentioned that you recently changed the pump. Maybe it's the filter?

Good luck bro!

Miguel