I didn't read all the 45 pages of this thread, but reading last two pages, it looks like a solution to this problem has not yet been found.
Hello Jack,
as you correctly deduced, the HSG is needed to bypass when shifting to 2nd gear on the electric engine. This causes the ICE to rotate because of the direct connection. When shifting for the first time after a break of several hours, this will start the ICE and it will run for about 3 minutes. Avoiding this shifting process, as you described as a solution, is a possibility. However, it is unsatisfactory to the highest degree if you don't want to become a traffic obstacle on the highway.
Contrary to your assumption, there is an update for a satisfying solution of this problem, which can be installed by your garage. This update has been installed and successfully tested on some ? of the members of this forum and also on my ?. With this update, the problem of the ICE starting unnecessarily is finally a thing of the past.