ganttproject.exe is generated with launch4j tool, and support of JAVA_HOME or any other way of locating Java Runtime from other vendors is basically up to them.
They have an open ticket in their issue tracker where you can also find a workaround with setting required values in Windows registry manually: https://sourceforge.net/p/launch4j/feature-requests/127/
Also, changing .gan file association from ganttproject.exe to ganttproject.bat works perfectly and makes GanttProject files opening with double click. This sits in HKEY_CLASSES_ROOT\.gan\shell\open\command
We understand that this turbulence with multiple Java Runtime vendors is sad. However, it seems that we all just have to wait a little bit until is settles down and all vendors and tools come to some common solution. From our side side we plan to ship GanttProject with our own Java Runtime starting from the next major update.