UPDATE: I recently used my last Kleenex from the “Kleenex Box of Sith[sup]TM[\sup].” I got a new, plain, square box of Kleenex and did a Kleenex-ectomy on it by carefully prying open the flaps on the side of the box. Inside were Kleenex, a stack of them, and the whole stack was folded in half. (Funny, I thought there was something a little more mysterious going on in there. If the long boxes are cheaper, next time I’ll just buy those and fold the stack in half.)
I then opened the “Kleenex Box of Sith[sup]TM[\sup]”, using my jackknife to ease through each blob of glue. Because the “Kleenex Box of Sith[sup]TM[\sup]” is has a slick, durable surface, the blobs remained intact and the paper did not tear. I inserted the new Kleenex and closed the flaps. The glue seemed to retain enough tackiness that I didn’t have to use any more glue or tape or anything.
Success!
Now if I can just figure out what to do about the silverfish.