I would "rough up" the plastic that fits in the tube-slots and use 15 or 30 minute epoxy.
Don't use that 5 minute RUBBISH.
Epoxy is probably the best for attaching plastic to cardboard. The resin in epoxy soaks into the cardboard, and roughing up the plastic allows the epoxy to "bite" better.
Plastic cement in any form is LOUSY for bonding plastic to cardboard.

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When in doubt, WHACK the GAS and DITCH the brake !!!

Yes, there is such a thing as NORMAL, if you have to ask what is "NORMAL" , you probably aren't !
Failure may not be an OPTION, but it is ALWAYS a POSSIBILITY.
ALL systems are GO for MAYHEM, CHAOS, TURMOIL, FIASCOS, and HAVOC !