I'm sure Paul Jensen has done at least one but I don't know what kind of a backer he used. On most of his boards he does a carbon laminate behind the strips. The carbon reinforced panels are fitted over frames. I believe Balsa planking is the covering on this quad swallowtail.
Balsa is probably your best option, but I wouldn't go thinner than 8mm.......................you'll need more support under the deck if you use the Jensen type frame , maybe full length stringers checked into the frame and faired into your deck..........and you should epoxy the whole inside to make it waterproof . Theres a lot of ways to do it ,you just need to have a clear plan before you start. Balsa will make a better surfboard if you do it right.
The reason for sealing the inside of a balsa board is to help protect it from rot. The difference in temperature on the inside and out can cause condensation or cause water to be sucked into the board if you have a pin hole. That is the weak point of the strip plank boards and chambered boards. If you have ever done repairs on chambered balsa board you would see they rot from the inside out. Paul Jensens boards being glassed inside and out helps protect from the rot inside. Also a sandwich of glass cloth,balsa, glass cloth is much stronger than even a thick stick of balsa. You can also flex a glass,balsa,glass more than stick of balsa. not to mention impact protection. Ahui Hou- Wood_Ogre
slp , you can simplify the frame , that one was way over-designed. you just gotta have good suport structurally under a hollow deck . Listen to Wood Ogre, he's on it, and he knows. Don't forget the breather hole and put bottom to deck suport for centre fin and sidefins(if you use them). The board came up good..........yet to ride it myself , but the owner said she picks up waves real easy and loves speed and power.