6GB is small but possibly possible for FC.
You can make life easier, when pushed for space, by not
allocating different partitions to / /boot /home /usr
That way, any free sace can be allocated as needed instead of an individual partition running out of space.
So: Repartition: Give swap 256MB and let / have the rest. No other partitions.
Then try installing.
My post #7 was spot on, from what you have posted as the output of df -h
Disks are cheap now, why don't you just get a bigger one? If money is tight, go to the recycling centre and help yourself to a few. Most will work