Yeah, I get that. I agree with you, screws would be better.
Indeed, this is the only join in this project that doesn't use screws exclusively.
But I can't have screw heads on the exterior, because I'll be putting the box on my lap sometimes, and I don't want it chewing up my pants. I'd prefer to, as you suggest, put an extra strip of wood in there for the hinge to attach to.
But really, there isn't room.
The hinge axis needs to be right at the edge of the plywood and near the outside edge of the box's thick back wall. Putting more wood under the hinge would mess up the geometry. A piano hinge wouldn't help because it still needs to fit between the floor and the back wall, with no room for extra wood. Putting a support block just forward of the back wall is more plausible, but there's controls and wires and stuff in the way, so it wouldn't be big enough for much strength. Also, I'd need hinges configured like this:
If I had hinges like that, I'd totally be using those, with screws and a support block. That would be the best answer. Then I wouldn't be here asking this question. But those things are expensive, when you can even find them; I don't have any.
So, knowing full well it's not ideal, I'm going to be using glue. Thus, I'd now like to choose the best glue for a bad situation, and I'm asking for help.
Now, with all due respect, you've just done that annoying Internet thing of second-guessing the premise of my question instead of answering it.
It's my fault, really - it is a weird question; I should have made it clear that I know what I'm getting into. And it is worth being very clear, for those who might come across this discussion in the future, out of context: Gluing metal hinges to plywood, rather than screwing them to wood glued to the plywood, is a bad idea. Le Chuck is right to say, "don't do that".
But I've considered many other options and none of them will work in this project. So, I'm forced to pursue this relatively inadvisable approach.
So, let's try this again.
I unfortunately need to glue these metal hinges to this thin plywood, alas, alas. What glue shall I try for best results?