Hi @pdehaye,
this is probably not the cleanest way to do it but it works: I generate and modify the jupyter_notebook_config.py file locally and upload it to Github. Then in postBuild I just copy that file to the right place. With that I manage to upload images of a few tens of Mb in the Binder session. Above that, uploading stalls.
You can find an example here: https://github.com/guiwitz/voila_image_processing/tree/master/
In this example, if you click on the Binder badge it will open a Voilà dashboard (https://github.com/voila-dashboards/voila) that works with ipywidgets. If you want a regular Jupyter session you can just take the regular route via the mybinder.org site.
I hope that helps!