Let's start with this part:
I thought Partimage was simply a front end to what could be done on CLI. But Partimage requires partitions to be unmounted to work whereas tar doesn't seem to care. What's the difference?
No difference in practice, as far as I can tell. That is why prefer to backup and restore using the CLI instead.
As for booting up to the restored installation, you have to change the fstab and menu.lst on sda11 (the new root partition) accordingly. And that is another reason why I prefer using the CLI from the Live CD to restore backups.
This editing must be performed because the fstab still points to sda2 for use as home partition.