I gave the Cookie House another try. I still did not use gingerbread, and I didn't try the shortbread again, but I used rice krispie treats. The house is still not picture perfect, but at least I was able to get it together. I used M&M's, peppermint striped candy sticks, gumdrops, mini white chocolate chips, and white chocolate covered pretzels.
What's not readily apparent are the bazillion toothpicks and wooden skewers running through the house to help keep the walls from collapsing. In fact in the picture below you can probably see one near the roof line on the right side. I did put the krispie treats in the fridge overnight before putting everything together and that helped just a little to harden the "walls". I would have put more decorations on to hide the worst flaws but I ran out of icing and didn't feel like making more.
Something else I didn't realize until I looked at the pictures is how crooked looking the windows look. You'll have to take my word for it that it's really an optical illusion from the candy stick stripes.
I would definitely try this again. Next time I think I'll make the walls a little thicker. And I also have an idea of making krispie treat "bricks"...