I found this website A brief introduction... - Guerrilla Money
It is pretty comprehensive but could not find anything about the overprint and stamps. It seems more related to the Imperial issues.
Could you ask the Navy or Smithsonian about the history of it?
I have personally seen the JIM notes going up in price recently. I have not seen a 1000 peso note before nor this type of overprint or the stamp on a JIM.
Just after the war was over the US military continued to back these notes as they did not have anything else to use. Even though the US had dumped counterfeit notes before the end of the war to create economic turmoil in the occupied countries.
Please, let us know what you find out about it.