I would recommend trying the standard technique first. I’m referring to reinforcing the hinge with hot glue. It very rarely fails unless you have a collision/crash, or if it gets hanger rash.
When the hinge fails, it’s not because the paper tears. It’s because the paper pulls away from the foam next to the hinge. This is why taping the back of the hinge doesn’t accomplish much IMO. The tape is just attached to the paper and it doesn’t accomplish anything when the paper pulls off the foam. Taping the inside of the hinge, as others have suggested, might be more effective. Regardless, the fix for this failure mode is simple. You just lift the paper away from the foam where it separated, squirt a little hot glue under there, and immediately push it down flat. At that point, it’s much stronger than it was originally.
Regarding the reinforcement technique, it’s difficult to get it right the first time. If you don’t move quickly enough, or don’t scrape enough glue off, you’ll end up with a stiff hinge. To do it right, first holds the hinge so that the inner hinge surfaces are just a little concave, like a 160 degree angle. The gives you a valley that you can use to quickly guide your hot glue gun down so that you can get the hot glue on faster. So then quickly apply a thin bead of glue. Next, open the hinge so that the inner surfaces of the hinge are slightly obtuse, like 200 degrees. Now very quickly wipe the glue with a square of foam. Because the hinge point will be slightly sticking out (because of the obtuse angle), your foam square will be directly rubbing on it, which is key, because that’s the most important place to clear the glue off in order to not have a stiff hinge.
Overall, it’s a very easy and effective process, but you have to get the whole thing done in under 5 seconds for best results. If the glue starts to set up before you’re done, you’ll have a stiff hinge. It takes a few tries, but it’s not difficult. Lastly, if you do fail the first time and get a stiff hinge, you can fix it by heating up a thin putty knife with a heat gun, and use that to scrape off the excess.
Good luck!