Some thoughts on this..
I myself would do the job using a LiveCD. This ensures there are no files open so no data loss is coming. Symlinking shouldn't be needed as far as I know, just moving the data and editing fstab to point to the correct location should be possible. In your case you could possibly even switch /var and /home since /var seems to be small enough to fit into hda6, and /home might need the space at hda7 at some point. Though if /var grows big some day, you need to do some tricks.
Unfortunately I have no experience on how multiple mountpoints on the same partition work (well I have some, actually, but it was unintended and I didn't study that much), but on the other hand I see no problem there. Switching /var and /home partitions would be my choice here.
Keep in mind, also, that if you're using LVM (Logical Volume Group), you'd better read how it reacts if you do a sudden change. LVM makes it possible to do some nice stuff but I've got no idea how it works in this case (sorry, haven't had time to get deeper into that yet).
If you were on a regular "good old" system, you could probably just (using a LiveCD, perhaps) move the /var directory contents to hda6 and /home to hda7, then switch these two in fstab, reboot and see if it worked. But nowadays with all these fancy systems around, taking care of your partitioning and mounting for you, it just might need a bit more care.
Good luck anyway, it shouldn't (no matter what it sounds) be a difficult task. After all it's all just about telling the operating system where the data resides..