I've solved many old style electronic injection system "hot soak" problems by drilling a VERY small hole, at an angle, through the pressure regulator seat (inside) allowing the vapors to be purged and allowing fresh fuel to enter the lines. It creates a slightly longer crank time at every start but you never have the hard start and rough, choking running when started hot. I learned this at my first dealership about 1979. This takes technical knowledge of the workings of the regulator and a steady hand but it works great.
The newer system, the CIS, is another matter and the fuel distributor can be a major headache. If you take off the air cleaner and push the intake flap down and see fresh fuel on the throttle plate, you have a leaking fuel distributor.....an expensive problem. Putting a pressure guage on either system and watching the pressure drop will tell you if you have a problem or not. Clamping the lines between the engine and tank, ( one at a time if you detect a definate pressure drop) can tell you if it's a check valve on the pump...another possibility in all benz injection sysems or the pressure regulator....or at a worse case scenario, a fuel distributor...which again you look at the throttle plate looking for any liquid raw fuel.