What kind of contactor or device do I need to keep a contactor closed until power draw of the primary circuit is complete?
Seems like you want a current-sensing relay that enables the contactor. As long as the remote load is drawing current the contactor remains energized. When it drops below the threshold the contactor is released. 

In order to start the process you would use another contact in parallel with the current-sensing relay, and only energize it briefly (you could use a time delay relay).