"Is there a software solution, like a file system or a file format, specifically tailored to avoid this kind of bit rot?"
Yes, ZFS is specifically tailored for this. Configure a zpool running RAID-Z2 with a hot spare or RAID-Z3. Half a dozen 6TB or 8TB disks should suffice.
Set it to auto-scrub regularly. Send logs and warnings to your email, and pay attention to them. (This is the hard part). Especially pay attention if they stop arriving. (This is even harder).
I have used Nexenta for some time, but the free product has a limit of 18TB of raw storage. If I was starting today I would use FreeNAS which has no such restriction.
The other comments about the futility of trying to do this long term are worth heeding, but that doesn't mean you shouldn't try. They key is to make this an active project rather than a passive archive, and to re-evaluate the best approach every few years.