Good clarification . I have done a research about the distinction between shall and will. Beside what you said above, it leads me to the following:
Sometime, we can use shall with a subject in the second or third person ( you, they, he, she and it ) in some situations to express determination, promise, obligation, or permission, depending on the cont ext. For example, "You shall leave tomorrow". This sentence has the ring of a command.
Many Regards