That looks great, 2Bits -- although I do see SOME wood in there.

Back in my slow-as-molasses world, I tested some more adhesive samples, this time with a full week of curing time.
Sika is a German polyurethane-based adhesive and sealant sold at Home Depot. Both products do not have Gorilla Glues 4X expansion property (which has positives and negatives to it).
In my testing, the sealant did a better job than the adhesive when it came to adhering a piece of Aluminum Composite Panel to 1" XPS foam and then to a 1/4"-thick piece of corrugated polypropylene. Both would work fine for this application, but were not the absolute best in this test.
Gorilla Construction Adhesive, which I think is polyurethane based, did slightly better than the Sika, at least in this test. In my destructive separation of the foam insulation from the Aluminum Composite panel, the foam broke up into pieces before the two pieces would separate.
But the traditional Gorilla Glue did even better than the construction adhesive. I'm still on the fence with Gorilla Glue, since cleaning up the expanded glue and dealing with possible bowing/distortion from that expansion might be an issue in adhering large wall sections. It works REALLY well, though. Very hard to get it apart without just chiseling away the foam:

Dow Corning 995, which is a structural adhesive used in glazing applications, has the advantage of staying flexible for a long time. I think for locations where continued flexibility is important, a mix of VHB tape and this stuff will be useful. But as a full-sheet adhesive, it wasn't quite as good as (either of) the Gorilla products.
The big surprise to me was Glidden Gripper, which is just a high-end paint primer that happens to be a fantastic adhesive for XPS and EPS foam. It was the hardest to separate from the Aluminum Composite Panel, hands down. I had to get a screwdriver in there and basically just tear up the foam to get the pieces apart. My questions with it are whether its limited ability to fill gaps (which Gorilla Glue is so good at) will be a limitation. Certainly for wall applications where I can use weight to clamp the two pieces together for a long cure time seem to suggest that it would make an awesome (and VERY cost-effective) adhesive for this project. My other question is whether there will be long term 'aging' issues for a latex paint product. But this stuff was great. Right up there with Gorilla glue and MUCH easier to work with (and MUCH less expensive, too).
I did the Glidden Gripper test after the others (I was priming an unrelated project with the kids), and didn't clamp it as well. But you can see the section where the foam came apart rather than losing adhesion, and another section that involved some gap-filling which was also very difficult to pull apart:
