However, it could still be due to a too-low starter motor speed.
Therefore: Observe/log these.
The reason why recoding some TDI engines to automatic mode can help is because it allows the engine to start at lower RPMs. When the coolant temperature sensor is disconnected, the engine control unit (ECU) assumes a very low temperature value, causing the ECU to interpret it as a cold start. During a cold start, any existing RPM threshold for starting is typically much lower, or even at 0.
There are various discussions about the "warm start" problem in this forum. Simply search for "warm start problem" and click through the similar topics (located in the bottom left corner of each topic).
Best regards, Rainer.