Most models have a process for restoring defaults without wiping data, it sounds like you found that process but it isn't working for you for some reason.
You have some options but you should proceed carefully if you care about the data on the device.
personally, I would remove the drive and connect it to a computer running linux and back up the data directly before trying to reinstall the firmware. The data volume is formatted as XFS and will be recognized by most distributions.
I believe the link you are talking about discusses re-installing the firmware to gain access. You should be able to do that by enabling the debug options of lsupdater and forcing a firmware reinstall:
https://buffalonas.miraheze.org/wiki/Enable_Debug_modeI believe you can force-reinstall the firmware (and in the process restore the default password in the process) without wiping your data but I highly recommend backing up the data first before trying it.