I just wanted to share my experience so that you are fully informed. I would not call an endoscopy invasive. I had my first one around the same age as your son and several more since. Yes, they give you medication to make it a more pleasent experience, however the recovery time is minimal. I had unexplained and inconsistent gastrointestinal issues. They found I had a hiatal hernia which was very inflamed. This then helped them form an appropriate treatment plan, which included aggresive medication to heal the inflamation. If the inflamed tissue is not allowed to heal, it can develop into a precancerous condition. This is what my dad has from years of ignoring his own GERD.
While I completely agree that traditional medicine does not always have the answer, I feel it is still important to consider them experts with your son's well being as their priority. I'm glad you are looking for another Pediatrician that is willing to be open to all possibilities. I'm wondering how yours would be if you allowed your son to have an endoscopy? Often times they like to rule out the most common things before they dig deeper. And even if your son does have a Gluten intolerance, his digestive track could be damaged because of it and still need to be treated. Does that make sense?
Just my thoughts and experiences. I do believe mommy intuition is by far the best thing out there. Keep strong for your son and I sure hope you can find a doctor who will be the answer to your needs. Good luck!