In Photoshop I would put all the background layers in a folder and drag all the foreground images above it. Then turning them all off but the one I wanted to save as a copy in the desired format. This way I can crop and move the foregrounds to my liking. Also I can adjust the blending.
The automation's options are quite limited (read: stupid). From a programmer's view I would make layer compositions of all foregrounds, turn them on one by one, export and then the next, etc.
In Illustrator I would place a link of the background image, copy the art board multiple times and place each foreground to its own art board. Afterwards I can specify which art boards I want to export before I am satisfied with all. And I can even make one big export if I untag art boards option.
You don't need to copy the art board 50 times or so if you rename the foreground files. Name the 10 foreground images foregr-01 to foregr-10. Now copy then in a folder set-01. Have different foregrounds with the same names in set-02 to set-05. Now you only have to rename your current foreground folder and relink the first foreground to the new folder upon opening the file.
If you want different backgrounds for each set, use the same file name.