Forget the screens - if they are plugged that bad - the car would never run. Have you checked the spray pattern of your injectors? Bad injectors could squirt raw fuel in so bad that the engine would have to clear it to run and it would run rough until the extra was cleaned out - similar to your scenario. Do you have any black smoke out the tailpipe when it is cold? Is the inside of the exhaust tip of your tailpipe coated in black soot? If the exhaust is good then it must be fuel starvation - I pulled up an older post about fuel pressure on a 300E -principle should be the same. I am pasting the response from Steveflb here in the hope it may help you:
You need to have fuel pressure for the system to work. You can't condemn the distributor till you have checked fuel pressure.
Does the airflow meter flap offer resistance when the pump runs compared to when its not running. The pressure drops in half instantly on fuel pump shut-off this is a distinct difference in the feel of the flow plate. Jump the fuel pump to test the feel with pressure (?). Also while cranking try pushing down on the plate massive misaddjustment can keep fuel from flowing till large plate movements.
Bosch Master, ASE Master, L1
27 years MB technician
Hope this is of assistance - keep us posted