yeah thats about what I did.. Im still using the carbon strips as sparing but the strength comes from the folded foam. If you're wanting to do shrink wrap I would suggest a carbon tube spar, and dont get picky with the weight cause the pla will always be heavier. Also pla is real bendy and pliable with heat. So here's the other two problems. I had major warping after heat shrinking and the wrap doest stick too good to prints. Since problem one was already a bummer I didnt think it a good use of my time to properly sand the pla perfectly flat. I thought about filler such as bondo instead of sanding but the overall result for me was longer and more tedious to build, heavier, and less stable than just folding a piece of foam. I full heartedly believe that if shrink wrap and weight is a priority for you than balsa excels at both much better than printing.
I do have a roll of carbon fiber htpla, but from what I hear, even after annealing, it isnt too much stronger than a regular print. I couldnt get the roll to print consistently but I did buy it for this kind of design concept thinking the fiber would line up and Id have a ridged piece along the x,y axis. Not going back to it tho. The trouble of design and printing doesnt out perform foamboard unfortunately.