You might try tacking down the corners with thinned Titebond. Apply it to the loose corner material and the balsa structure, let it dry, then iron it down. I use this procedure on veneers and it works great. As for the painting-you have some restrictions that will be difficult to overcome, namely an apartment, asthma and the inability to spray bulk products. With all that said, Minwax water based polycrylic may come in handy. On a recent build, I sprayed hi fill Duplicolor auto primer over Solartex, color coated with latex paint(sprayed through a gun), coated with polycrylic, and clear fuel proofed with Lustercoat. The polyc acts like a barrier to protect the latex from the hot solvents in the Lustercoat. Sufficient drying times between products is very important here. If it were me and I didn't have a place to spray using a gun and compressor, I'd use colored fabrics like Coverite, but that's just my .02 Hope any of this helps.