Yes, I know all this - read it. What you also see in the starting aid section, is that MB were struggling a bit with hot start and were modifying it along the years, including the last modifications on version III (early and late) of staritng aid, which is to give 1 second impulse to CSV above 35 degrees. At some stage the solenoid on FIP was helping, then it was gone, something had to take its role when hot.
The modern Bosch TTS replacement (unfortunately looks different than original) has electronics inside and gives impulse even at high temperature. Works perfect. Anyway, it is all activated when the ignition key is turned on.
Look, I am not qualified enough to argue the point. I am just sharing my own experience. If your TTS works properly (which is easy to check) - then it is fine. Please do not take any cost involving action if you are not convinced. It may be something completely different (air buffles in fuel lines? caused by too high temperature?). I am assuming that you have all other things (ignition, mixture, linkage and valves related) under control. Are you using the proper spark plugs? Are they in god condition? I guess these are the usual suspects...
I just thought: if you are saying thet the trouble is there when you immediately try to start after engine stopped (traffic lights) then maybe indeed I am on a wrong track. If you leave the car even 5 minutes - it cools down a bit, not much, but a bit. Disregard it then, it must be something else.