I have a 92 300sl with the same symptoms as your 300e. I took it to a mechanic who replaced the fuel filters, checked the fuel pumps and determined the rough starting was caused by the injectors. Instead of replacing them he cleaned them and told me to drive the car. It didnt run much better. ($400 later)
He told me the next step would be to replace the injectors. (another $400) It looks like a easy project. Please let me know how you job turned out.
p.s the prevoius owner of my car took it to another mechanic who replaced the timing chain and then told me the next step was to replace the fuel pumps. Its hard to find good mechanics.