I searched for 'saliva SLGA' and I think the websites will answer your questions. I didn't have any hits for SIGA in saliva.
In some people the anti gliadin antibodies come back to normal slowly. After eating gluten the autoimmune reaction can last for about 3 to 5 months when the cells have stopped producing the antibodies. Some people have plaques of gluten in the intestine which may provide a source of gliadin. It may be possible to eat away at these plaques with digestive enzymes. It is difficult to eliminate all sources of gluten. You may be one of the people who reacts to tiny amounts - flower dust in kitchens, plaster, talcum powder, some powdered sugar, etc. Some products labeled gluten free contain 3 to 8 mcgs of gluten, enough to cause a reaction in sensitive people. People at Celiac.com forums can tell you more about FDA labeling requirements for gluten in foods.