John,
Thanks for finding all that you listed.
I don't know if that is the same man or not. I suppose it is possible that a Sergeant J. Drury Pulliam could have been promoted to captain as reward for returning to Union -occupied Missouri to recruit. I have seen records where men were promoted for taking on that dangerous assignment, so it is possible.
It is also possible that more than one J. Drury Pulliam served on the southern side.
This has me baffled.
Bruce