Have looked into balsa too and came to the same conclusion as you. There are some types of cedar that have low density. Check it out if you want to shave weight off a wood construction.
The long cuts are made using the hot wire cutter fixture described above and the short cuts(each piece) is done by hand using a sharp kitchen knife.
Make sure the foam you use is dense enough. I wouldn't use anything lighter than what I have, 32kg/m^3. Denser is better..
