Is it possible to run a python script(with a Python IDE) that takes data from a Blender file and gives some results without running Blender itself?
Im a total begineer at Blender, but I've got some technical knoweldge as a developer. If you don't find any solution, I think you might be able to install blender on a remote server (with a graphical user interface). Then import your file and then find a way to expose blender operations as a server. However if the main problem is to support a better python IDE than the one embedded in the blender text editor, I have no clue for that :/
I think you might be able to import bpy in you python IDE to let it detect blender symbols (bpy.context, bpy.data ...) but you'll still have to copy/past your scripts inside text editor to run the full script