From the help file:
Select Specify target field or click Specify to specify the field to be exported. If no field is specified, FileMaker Pro will export the contents of the current field in the active table.
So it might be possible to do this by not specifying any field at all if you can figure a way to put the focus in the correct field--such as a layout with just this container field and Go to next field used to put the focus in it. Not sure that's a whole lot simpler than multiple copies of this script step with different field references, but it's all I can think of....
It works if you can get the container field selected by making it the button but it's very fragile. I'll probably go with the bazillion scripts for now.
Or just one script with a "chain" if if/else If steps to select for a specific Export step.