Yeah, I would try the liquid nails. Try to get some liquid nails in between the the sidewall and the base. I would shoot for a little bead about every 3 inches or so. Liquid nails is not really flexible when it dries, so if you run a bead down the whole length of the ski, it may dramatically change the flex of the ski. That may not matter, but .... Once you have the liquid nails in and the edge back, use a bunch of clamps to hold it together while the liquid nails dries. Use something like a big C clamp and have the clamp going across the base so it is squeezing the 2 edges together, Make sure you clean off the excess liquid nails that seeps out.
Honestly, I have never attempted this or seen anyone try it either. I am basically pulling this out of my ass, but this is what I would try. Should work for back yard jibbing at least for awhile. It's either that or pitch them.