von Ken Task.
Current site is an Edu and appears to have many courses - how many? That also means users - how many?
The direction you are taking ... restoring course backups from a 3.6/7 to a 4.5+ seems to me isn't the path of least resistance, but there could be other reasons for such.
In that light, mind sharing some more info ... since you have command line access to both servers.
Old server:
uname -an
free
df -h
New server: same commands
uname -an
free
df -h
'SoS', Ken