Wheat flour is fortified with vitamins in the U.S. as a part of USDA policy. Gluten free facsimile products are not fortified. There is no government mandate for such. When you remove wheat flour by going gluten free, you may be removing a significant source of vitamins.

Okay.  That doesn't answer the question, but thanks anyway.

A confirmed diagnosis of refractory coeliac disease is required to participate in the study unfortunately. Apologies you are feeling miserable even though you have remained gluten-free, I hope you are able to receive further understanding as to why from the relevant medical professional. I am hoping to provide copies of the content used in this study following its completion end of this year so will make a note to post on here when the study is complete, a copy of the resources used from the group. 

Do you think it’s a vitamin issue that could make celiac symptoms worse during recovery ? 

Multivitamin products are seldom potent to offset the vitamin and mineral deficiencies that typically result from long term undiagnosed celiac disease. We commonly recommend sublingual B12, a B-complex 5-10k IU of D3, 400 mg daily of magnesium glycinate, and zinc picolinate. The forms of certain vitamins like magnesium and zinc are important since it has a significant impact on absorbability. If you live near a Costco, the Kirkland Signature series and Nature Made lines are good quality choices and economical. And they will indicate on the packaging if they are gluten free.