If you're worried about the nut-sert not holding onto the plastic that well, you could always remove that broken stud, and then drill an access hole near where the stud was. you could feed another bolt through, and with a little patience, get it sticking out of the original hole where the stud was. You can use a pushnut washer to hold the new stud in place. Once done you can then plug up the access hole with a rubber plug if you'd like.
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