I agree with you about the risk of stasis. Cardboard & paper have glues & inert chemicals in them to make the wood pulp hold together. These are
not poisonous but prevent proper break up of the wood pulp in the gut, so they are more prone to blockages.
In addition to what others have advised about check ups, etc. I & others found that free feeding Thumper bunny safe tree leaves with his hay, satisfied his craving for wood pulp safely.
It is said that the craving for woody fiber can be a sign of an inherantly slow gut particularly the caecum. Tree leaves seem to help to correct this.
I would also say that to help them to overcome the cardboard
habit & latch on to the tree leaf habit we sometimes have to remove cardboard from them, until they get the hang of eating leaves instead. Most buns prefer hawthorn which is thankfully comon.
There is another behaviour of trying to enlarge entrance holes to safe places, so they can turn to hide in a box more quickly. They often try to "round off" 90 degree corners as well. This is to reduce the risk of a potential predator from ambushing them from behind a sharp corner.
My bun still tugs up carpet 6 years on, but only when he's frustrated now. He stopped eating it when given tree leaves & is completely safe with cardboard.