https://www.hetzner.com/dedicated-rootserver/matrix-sx
(You would need 4 SX294s for half a petabyte with 2x replication)
And put ceph on them which gives you an S3-compatible API:
https://docs.ceph.com/en/quincy/radosgw/index.html
It's not trivial to set up but once you do it's much cheaper than AWS. It's even cheaper if you can find the machines in the server auction. There are some 150 TB machines on there right now for 174 euro/month.
Also, your math does not quite add up if you want to store 425TiB. You'd be filling up the Ceph cluster to 95% which would be impossible (you'll start losing OSDs way before that).
If this was me, I would definitely do this on Ceph, but I would opt for a more traditional erasure coding setup of 8+3. For that, you'd need 12x SX134s as a minimum starting point.
I suppose you could start with an EC profile of 2+2 or 4+2...
I do have a serious question on Hetzner:
Do they offer any private networking options? That page only lists a single 1 Gbit connection. I don't think that would work well with Ceph. It's doable, sure, but I wouldn't want to support such a cluster, not with 160TB raw per box.
Doesn't seem like it for their dedicated servers, not 100% sure though.
Their docs indicate that upgrading the 1Gbit ethernet link to 10GBe is an available option:
https://docs.hetzner.com/robot/dedicated-server/network/10g-...
Extending with additional NICs should be possible from what I've read but not used myself.