Once you've mounted the Wubi drive as a loopback like you described
earlier, you will be able to transfer individual files. You will be
able to browse the drive in Nautilus just like you can browse through
any folders in Ubuntu. Look for the mounted drive under "Places" if
it doesn't show up on your desktop after mounting. If you want, it
should be no problem to fill up the SD card, then finish off with a
thumbdrive or whatever else you prefer, if there is still more you
want to copy.

Then consider these all as backups. Once the fresh install completes,
remount the Wubi /home, and copy the whole thing over to your new
/home. Also, don't forget to reveal the hidden files (Control+H in
Ubuntu live CD, or click on the eyeball in puppy) to make sure you
have the things relevant to your various settings.