B.R.
Most allergists will do an oral challenge in their office only if there is evidence from the tests that the patient has outgrown an allergy. I've heard of oral immunotherapy for peanut allergy (giving small doses of the protein and very slowly increasing the dose in order to build up a tolerance), but that is still in clinical trial at Duke University, run by Dr. Wesley Burks. I've also heard of sublingual (under the tongue) therapy for some allergies. Have you contacted the allergy clinics at the major Children's Hosptials in Columbus, Cincinnati and Cleveland? They may be able to point you in the right direction.
About intestinal bleeding... Food allergies don't cause bleeding. My daughter (who also has multiple food allergies and eczema) had a bout of bloody diarrhea and was diagnosed with ulcerative colitis last year at age 4. You may want to get a referral to a gastroenterologist about the intestinal bleeding. My daughter also became anemic and had to have blood transfusions. Feel free to contact me if you would like more information. I can also recommend some supplements that can help to heal the damaged intestinal wall and an iron supplement that will not cause damaging oxidation in the intestine (don't use ferrous sulfate--use ferrochel). My daughter is now in remission from the UC.