If you can get the balsa core to set in place with thickened epoxy (and lots of patience holding it in place until it kicks) to hold you can put the glass back in the same way (i.e, half kicked thickened epoxy troweled on and push the glass into it. Do it in manageable sections and use a bunch of plastic thumbtacks/t-pins to hold it up until it starts to kick then use regular epoxy and a roller to wet the glass out. Leave the pins in place until it's solid, then grind off the heads and smooth the interior as needed. Finish it with paint or a vinyl liner if needed.
If you do it in sections you may want to do seams, or one big sheet over the whole thing. It's about strength not fracture lines.
If you really want to go esoteric - vacuum bagging won't work in your situation but a balloon might (blow up mattress anyone?) Test first, your results may vary
Remember the epoxy secret - epoxy doesn't stick to wax paper or waxed surfaces. Use liberally, often and before you THINK you need it.