According to this primary source document
the US had a third atom bomb ready to be
shipped as of 8/13/45, and could have produced
four more by 10/31/45:
http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB162/72.pdf
The General Hull in the link would be Lt. Gen. John E. Hull who was
then Assistant Chief of Staff of the War Department General Staff,
and Director of the War Department Operations Division. I do not know
who Col. Seaman was; it appears from the link that he was connected
with Los Alamos.