I can not believe that they would have overlooked this as a cause as blood work would have been made during the hospital stay. But I would be very concerned on his condition and the fact the doctors do not seem to have any clear cut ideas concerns me. The biopsies of the polyps may give some insight but the bleeding from the nose and rectum can be associated with some conditons as well.
Read over this and let me know if you feel these match his primary symptoms.
As you can see the liver can and does have major blood relations throughout the body and this very well could be his problem.
This can lead to varicose veins in the stomach and esophagus (gastric and esophageal varices) and rectum (hemorrhoids). Gastric and esophageal varices can rupture, bleed massively and even cause death.
From the link above if read fully.
Other then stomach ulcers or other upper or lower gi problems I can not suggest other options to the problem.
Please reply back if you need me.