Hey Gilles, a couple more options you can try, after reading many posts on S1mp3.org forums it appears some have had success by first reformatting their players before flashing the firmware.

Also most of the firmware on the net are not full firmware files but partial dumps. I found this link to a firmware file that has the same image content as the first one you downloaded but is claimed to be a full firmware file might be worth a try.
http://www.alexejw.net/firmware/MP-6...5.35%20full.7z

Fingers crossed,
Terry