In both books the authors dicuss the sessions in which the office of President of the United States were discussed. There were several competing ideas, including a triumvirate and a President by Committee. Indeed, the idea of "national" office occupied by a solitary individual was very distasteful to some delegates, as it was too close to the idea of a king (who they had dumped just a few years earlier). So I think it is incorrect to suggest that the powers of an existing office were simply being "expanded." I see the Presidency as novel for its time.
The Constitution created a new office, which embodied both the executive power of the government and the role of chief-of-state, without conceding the legislative powers. Hanson and his fellow "presidents" were, in reality, only presiding officials in a governmental body.
But it always makes for a good discussion!
Also, according to indorsement, was read a letter from the Secretary for Foreign Affairs, forwarding a letter from the President of Pennsylvania, Benjamin Franklin.