Thanks for the recommendations on adhesives, Howard. There are many good ones out there, some better than others (i.e. be wary of glues described as "all-purpose"). Sometimes you have to pick your glue based on the what and how you are gluing. For much of this project, I have returned to Titebond's original wood glue. It's similar to Elmer's All-Purpose but it get tackier faster and I think it bonds tighter and stronger. I've had good luck with the extra-strength glue-sticks when gluing up paper and card-stock. Not sure why it didn't work this time.
To try and straighten up the sides of the fortified house, I'm using Weldwood contact cement. Apply it, let it sit for fifteen minutes or so, than attach the bits and clamp it with a few rubber bands. I usually get a good strong bond with Weldwood, and this is going to require one. Cure time is probably 24 hours. The critical part of using Weldwood is making sure it's mixed...some of the bonding agent has a tendency to settle to the bottom of the can or jar, and mixing it can be difficult. If you don't get it mixed, however, the bond will be significantly weaker.
File comment: Fortified house straighten
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I tried using Gorilla glue when it first came out. It's a polyurthane-base, so you have to wet the surfaces of what you're gluing to get the best bond. I will admit, I tried using it on furniture construction/repairs, where stress can be amplified. It didn't seem to work very well, crystalizing over time and eventually coming apart. Plus the shelf-life is short...seemed bottles of the stuff went solid in a matter of weeks.
My current favorite glue is Loctite GO2. I've used it on everything - paper, wood, metal, cardboard, ceramics, and a few others, and it seems to hold up well. I haven't used it on any furniture or load-bearing joints. It's a bit of a mess to clean up, though, as it's not water-based.
When everything else fails, you're right, epoxy is the place to go, especially in the marine variation. That's the ultimate bond.