Answer: Balantidium coli
This parasite is unique in 2 aspects: it is the largest protozoan parasite and the only ciliated parasite to infect humans. Like amebiasis, the site of infection is typically the large intestine, where it can cause invasive disease, bloody diarrhea, fever, and abdominal pain. This case is a good example of invasive disease with mucosal ulceration (below).
Within the ulcer and intestinal mucosa, the large ciliated trophozoites can be seen.
The trophozoites are large (typically > 50 microns) and have a vacuolated cytoplasm and a classic dark "kidney-bean" shaped macro-nucleus. These features allow these trophozoites to be distinguished from those of Entamoeba histolytica, which are smaller (20 microns) and have a smaller, less distinctive nucleus. In the image below, only a partial cross-section of a trophozoite is seen, and so the full diameter is not appreciated.
A second trophozoite shown below is clearly larger and is surrounded by a "fuzzy" layer, which represents the cilia.
Here is an image from a trichrome-stained fecal smear that more clearly shows the "kidney-bean" shaped macronucleus and surrounding cilia.
Finally, Dr. W. reminds us that Balantidium coli trophozoites have a particular type of motility. She states "When I first encountered this parasite as a path resident and learned that its motility was "boring", I thought that meant that the motility was uninteresting". Indeed, the motility is "rotary" or "boring". Great story!
Thanks to everyone who wrote in with comments.