Fun and Games!
The backups from older version of moodle might contain content from modules not installed in the 4 - or not compatible with 4.
Investigation: the backups are .mbz - gunzipped. Un-archive on local computer in a test directory. Among the un-archived files, there will be a moodle_backup.xml file - it's the 'road map' for restores. In the head of that file, it will provide what version of Moodle that course backup was made from. It won't, however, indicate a module used in that old course that is no longer supported in 4.
moodledata/temp/backup is the directory where this work is done initially ... so that directory needs to have global all permissions.
You might look in that directory for failed restores - a contenthash named directory and inside there the un-archived contents of that backup.
6 Gig is large ... got Linux? Install moosh ... it has a command to restore courses to a category ... advantage in using moosh for such, no web service needs tweaking ... it's just moosh (a php script) and the DB.
Also, 4 is new ... just yesterday a 4.0.2 was released. Not sure if there was anything specific to restores of backup, but that did contain fixes. If your moodle was installed with git, suggest updating and keep the 4 to latest/greatest ... with fixes!
'SoS', Ken