Setting the logs to DEBUG wasn't an attempt to fix the export problem, but rather get more information about why it's failing. Can you look at the structure of the <install directory>\framework\etc\arcgis-logsettings.json file? Does it look something like this?
{
"logDir": "C:\\arcgisportal\\logs\\",
"logLevel": "WARNING",
"maxErrorReportsCount": 10,
"maxLogFileAge": 90,
"usageMeteringEnabled": false
}
If it does, I suggest you contact Support and have them take a look at the machine. Once you get the logs working, try to take another backup with Server logging DEBUG logs and share the logs here, or work with Support to figure out why it's failing.