I would go for all gluten. You will make mistakes at first. If you get improvement on all gluten, then you could try adding back in the non-wheat gluten to see if it makes a difference.
Several years ago, I tried to be gluten free to see if it would help with my migraines. I didn't worry about natural flavors, malt, or hidden gluten but I did get rid of the obvious gluten like bread and pasta. I did it for several months and didn't notice anything. When Girl Scout cookie time rolled around, I started eating those and that was the end of my gluten free trial.
Last year, I went completely gluten free. Since easy child was already gluten free, I was able to be extremely strict right from the start. Within 2 days, I knew I did not want to eat gluten ever again. I actually started the diet thinking I would do it around my children and cheat when I went out to eat without them. I feel so much better that I am not even tempted to cheat. I didn't even think I had symptoms from gluten but now that I know what I am like off gluten, I can say I had irritability, brain fog, ADD-like symptoms, fatigue, and depression. Traces of gluten bring that back on for more than 2 weeks.
If you only get rid of wheat, you will not have the chance to see what gluten might be doing to your child.
How about fruit rollups, potato chips, candy for processed food? My kids also take Dora the Explorer cereal to school as a snack and all their friends like it. Some have even started buying it themselves even though these kids are 9 and 11.