I actually have had physical boxes with Hetzner, as suggested by the author, for over 10 years, and ran multiple projects on them. Of course I had my share of disk failures. You tell them the disk serial via a special form, tell them when the necessary downtime for the swap is least disturbing for you, and someone switches the disk as requested. 5 minutes later the machine is up again, you trigger RAID rebuild, and that's it.

Doesn't cost a dime to do this, and not more than 20 minutes of work and 10 minutes downtime from my side.