Fairphone does not boot up anymore (bluescreen)

Since a couple of days my FP1 second batch freezes when turned on: it halts indefinetely on the blue “Fairphone” screen.

I managed to boot in recovery mode as described here https://fairphone.zendesk.com/hc/en-us/articles/201134418.
I wiped the cache, but the problem remains.
I reinstalled the OS with the procedure suggested above but still nothing.

Before resetting all the data I wanted to make a backup but I had this problem: in recovery mode I start the backup procedure and it tells me it’s copying about 12 GB on a empty 16 GB SD card but after a long time it raises a generic write error. I suspect this has to deal with the file system of the SD being FAT32, so the maximum allowed file size is 4GB.

I tryed to format the SD in Ext4 but the recovery mode doesn’t seem to be able to write on such file system.

I also tryed to connect to the phone with adb but the only mode I can obtain is the sideload mode.

What else can I try to make a backup of my data (actually I already have a copy of everything except the pictures) before resetting the phone?
Anybody knows if I can install a different recovery sw using the sideload mode?