Hi srego,
There is now build in functionality in GPF to do this. But it can be easily done in a command line script or a python script.
Even with Excel it is possible:
Have you already seen the guide on how to do batch processing?
You find an example graph in this post:
You need to get the bounding boxes once for your shapefiles. I hope there are not too many.
Unfortunate using a shapefile for creating a subset is not yet possible.
The shapefile the bounding box and the product can be parameters to the gpt call.
I hope this gives you a starting point to do your extraction.