Wait, is it gluten you're avoiding as an intolerance or some of the grains produce IgE-mediated symptoms? For IgE-mediated it is not only the gluten proteins that are allergens, there are more proteins than gluten. See related threads on barley and many of the problems in calls to manufacturers members have had because barley is not covered under FALCPA and for a gluten free certification it merely needs to meet a PPM for gluten only, which also will not include any testing for the presence of oats.
Additionally, I see you do not have barley listed as an allergen. This does happen in IgE-mediated allergy. There were a couple of members who had to avoid barley but not wheat because they dis not have cross-reactivity. Buckwheat does not have gluten but barley does... where that leaves you I'm not sure because I have no idea what you're avoiding and why based on the list and requests you've made.
The largest single population that I know of with IgE-mediated allergy to buckwheat is Korean but that could be somewhat attributed to prevelance of buckwheat in native diet. Barley is very closely related to wheat and rye. Oats is further out botanically but still related. Buckwheat is related to rhubarb. It is often used in gluten free products as it does not contain gluten. It is also not required to be listed under FALCPA. Extra caution would be needed.
Not being allergic to barley would open up a lot but as it contains gluten it won't be labeled gluten free. So it sounds like you might have a silver lining there.
The other health related reason to tease out the conflation of IgE allergy to wheat, barley, rye (and oat where it presents) from Celiac is the two require different management and treatment from two different types of doctors. IgE reactions may be outgrown but Celiac will not.