You have made it very difficult for yourself, and the basic problem is in fact all yours:
1. Why would you work without a backup of your personal files, bookmarks etc? You could just have a couple of backup flash media, and use something like
Code:
rsync -axu ~ /media/sdc1/home-bu
every now and then.

2. Why didn't you exploit the real great strength of Knoppix, the "large compressed basis + small (relatively) modifications" concept to your advantage, and turn it into a problem instead?
Again, you could have used (for example) the Install Knoppix to flash media function to make a backup to a couple of sticks/cards, and then every now and then issued an rsync command similar to the one above, something like:
Code:
 sudo rsync -axu /mnt/system/ /media/sdc1
Normally, that would just backup knoppix-data-img.

3. The simple system copy above allows for very safe experimenting. Keep track of disk use by issuing the df command often. (You have used that, right?) When modifications start to fill up persistent store, keep one unfilled copy as a backup - you will always be able to return to that point, if things get messed up. And you have separate backups of your home directory, so you should always be able to reconstruct most of your personal stuff when backtracking.
Always be prepared for backtracking!

4. When the Debian package tools have lost track, or you suspect they have, be very careful to use them, in particular for deleting packages. Try if you can get them to work properly, for instance by giving them the disk space they need, and if necessary, backtrack. And ALWAYS start install or delete operations with package database update, for example
Code:
  sudo apt-get update
5. Get to know knoppix-data.img. It is simply an ordinary file with an ext2 (or maybe ext3) file system setup on it, and loop-mounted. You can always mount that outside the native Knoppix instance (for example, from another Knoppix instance) and do whatever backup, cleanup, modification is needed. Just be aware that you should restrict writing/deleting, as then unionfs-mounting with aufs may get disturbed. Be particularly careful about deleting stuff you don't know what is. If you have a Knoppiix instance on /media/sdc1, something like this should be possible

Code:
sudo mkdir /tmp/persist-sdc1
sudo mount /media/sdc1/KNOPPIX/knoppix-data.img /tmp/persist-sdc1 -o loop=/dev/loop7
df
ls -alt /tmp/persist-sdc1/home
sudo rsync -axu /tmp/persist-sdc1/home/ <somewhere to place a backup of home disctory>
6. If you like to work minimalistic, practice resizing of persistent store so you can do that with no fuzz. Myself, I have been very much on the defensive side, always starting with a 3.5-4GB persistent store and never filling that up (thus having no experience with your problems, in spite of years of Knoppix use). But it may be better to start out with smaller store, and resize as needed. Will also make backup of the whole file run faster.

Have a lot of good luck!