Well, is "a ton" a level that can fit in a dedicated server or many? Just looking at https://serversearcher.com you've got 72TB of storage on 10Gb pipe for $360 or so a month: 128 GB RAM 6c/12t E-2276G 2X 512GB NVME + 4X 18.0TB HDD 300TB / 10Gbps

Just a few PB, and sharding it across servers is fine.

It looks like all the disk-optimized examples on that site (still much more expensive than paying for raw disk, barely 5x cheaper than S3, when a disk-optimized colo solution only has ~3% overhead over the disks themselves) are through some no-name provider "HostKey". I suppose beggars can't be choosers, but in the contexst of storage (where systemic failures should be accounted for in the model) are you aware of more than one provider with reasonably priced storage?