Ok, so in order to get at least a faint idea of what I'm talking about, I downloaded latest iso of DSL. I burned it, booted from a cd and made a USB pendrive install on a 128MB flash disk. It didn't give much chance to influence partitioning of the USB drive, but I could do that if I created the bootable USB manually.
I booted from the usb and, indeed, the output of df was similar to the one posted earlier. in fstab and mtab, however, the /dev/root was (if I remember it correctly) /dev/sda. The distro is on one of the partitions on the usb in the form of image, so I guess there's no simple way to change its configuration except for modifying the image or making your own distro. I don't have much experience with the unionfs, but I guess that the layout of the system is partially in RAM and partially on the usb drive.
The /root (root's home folder) indeed has 2.9 MB available with over 600kB already used. It seems to be a filesystem that doesn't exist physically on the usb drive, so repartitioning will probably not work here. I was, however, able to create 100+ MB files in /usr, /bin, /lib and /home/dsl so you can install additional software if you need it or store data in the regular user's home. If you need to save something that will not disappear after reboot, you can save it on the 1.8GB partition of yours. The only limitation is the 2.9 MB in /root which does not really matter since you shouldn't work with the usb system as root anyway, just use sudo instead.
So my advice is: just deal with the 2.9MB /root it does not limit you in any way. If you can't deal with it, try another distro.