Answer: Hairs, shown in cross-section
We believe that these structures are most likely hairs that have been ingested by the host (i.e. trichophagia) which could have potentially obstructed the appendix and resulted in appendicitis. I had not posted the answer until now because we were hoping to be able to prove the identity of these structure by staining them with keratin immunohistochemical stains and showing that they were refractile using polarized light (as we would expect to see with human hairs). Unfortunately we have not been able to get a hold of the slides again and therefore I will addend this post once we have conclusive evidence to share with you.
Thank you to everyone who wrote in to help with this case. We got a lot of great suggestions, with most readers agreeing that these structures were not parasites, but instead represented some type of foreign material. One astute reader also suggested that this could represent adiaspiromycosis, an infection by an aquatic protozoan parasite that can cause mass-like lesions of the nasal and ocular mucosa. Indeed, this case has a similar appearance but lacks the characteristic sporangia and sporangiospores. (You can see a case of adiaspiromycosis HERE).