I would diverge a bit:
1) reformat /dev/hda6 as ext3
2) install new linux putting grub/lilo into root partition (/dev/hda6 NOT the MBR)
3) I wouldn't share the home partition because significantly different linux distros may cause some weird behavior and you (or the system) might end up overwriting some things you didn't want to since you'll have write permission.
4) Share the swap space
5) Change the lilo in your Slack install to chainload the new lilo/grub (that way your slack partition should always be bootable and when you remove /dev/hda6 or install a new linux, you can keep it independent).
Anyway, that's my
