I would try gluing the liner while the binder is half closed.
If it's fully open and you glue it like that, then when you go to close the binder the liner which is on the inside of the curve is being compressed.
Now, if you were to glue the liner while the binder is closed, the opposite would happen. if you open the binder, then the liner will be stretched taught, while the outside is compress and gets wrinkled up.
Both, the liner have some give in terms of stretch and compression which is why I suggest trying something in-between. The result may still be undesirable though. you'll just have to try.
Another approach is to not glue the middle bit at all. It will lay down flat when open and then (hopefully) make a little bump when closed.
open:
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closed:
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