in trying to experiment on possible solutions for rough idle and cold start issues on my 91 560SEL, I found that adjusting the set screw in the EHA affects the 2500RPM behaviour mostly with very little change in the IDLE behavour. The opposite is true with the set screw in the mixture Tower.
Adjusting the mixture in the Tower affects IDLE behaviour mostly, with very little change in the 2500RPM behaviour.

Going back to your original issue of warm-start difficulty, a lot of postings point to the fuel accumulator as a probable cause.