I lived under a hail of discarded reproductive organs
Some of the glues contain boron. Like copper, cobalt, selenium, etc. life needs a moderate amount of this micronutrient, and has trouble dealing with an excess. I know of no easy and straightforward test for boron, so I use cardboard sparingly.
The only other toxicity issue I have heard of is that some blue inks contain copper. A flame test for this element is incredibly easy: small samples will burn with a bright green flame. I know there are agricultural uses for copper slufate, and so compost that includes these pigments might be of particular use somehow.
Glossy paper or office paper might have enough chalk or clay mixed in to slow down the process, but this is less of a harm than an obstruction.
I know that compost is very slow at digesting polyethylene (though appropriate bacteria have been identified), so I was surprised to learn that paraffin wax composts very quickly, provided it can be kept moist. Similarly, inks and glues decompose just fine.
Another idea for letterk: contact the garden services, and see if they would want to deliver browns to you. Where I am, they advertise free mulch extensively, hoping to avoid tipping fees. What sort of palm trees are these, that don't shed? I lived under a hail of discarded reproductive organs and fronds for years back in San Diego.