As mancerayder says below, why can't you back them up to an external USB drive? I rsync my 'archive' partition (photos, videos, music, programs, etc) daily to several external 4TB USB drives. Those are dirt-cheap these days. The process takes maybe 5 or 10 minutes depending on whether or not there have been any new files to transfer in the last 24 hours.

I refuse to relinquish my files to some insouciant third-party. And what recourse would you have if they lost them?? Very probably them saying "Sorry. Not our problem."