Sorry man, I think the API is the only way to get an output like that.
I work for a VAR in Minnesota and just to confirm that is correct there is no way to do this through the UI. I wrote an application that our customers and us use that accomplishes this. The tool will copy permissions from one vault to another as well as save the permissions out to a file. However if you are doing this as a form of backup it is not necessary as the EPDM SQL database contains all these permissions so if you are backing up your SQL database then you would be covered.
That what I was thinking but was not sure. This is not for backup, this is to move folder permissions form the "Test" vault to the "Production" vault.