Plesk Server Error 500 when downloading cloud back-up to server

The following describes an issue I encountered on our Ubuntu installation with Plesk 17.8.

Plesk 17.8 backup has the option to store locally, via FTP or in the cloud. When trying to move a backup from the cloud to the server using the Copy to Server Storage (Home -> Tools & Settings -> Backup Manager and then choose a cloud backup instance), it'll download it by default to the root folder. This filled up our root and caused the following error when trying to use Plesk:

Server Error 500
Plesk\Exception\Database
DB query failed: SQLSTATE[HY000]: General error: 1030 Got error 28 from storage engine, query was: DESCRIBE `sessions`
Type: Plesk\Exception\Database
Message DB query failed: SQLSTATE[HY000]: General error: 1030 Got error 28 from storage engine, query was: DESCRIBE `sessions`
File: Mysql.php
Line: 53


After that, sites started going down and general mayhem followed. After searching for solutions on the web, I was led to look in the /usr/local/psa/tmp directory. There, I found a file roughly the size of the amount of disk space I knew we had free before the incident. Its time and date also very closely matched that of the crash. I deleted it, and the system is back up.

Previously I tried restarting Plesk from the command line, but that didn't do anything. I read that a system reset would do the trick, but didn't want to chance trying to do a boot-up with a full disk.

I'd still like to transfer the cloud backups to our FTP server, but am not sure where to change the path so it doesn't fill up root. Any help is appreciated.