What I used to do for my autistic kid with the insur co was to get the specific numbers that they use for insur billing from the dr's office of the tests that they would do and the cost of each test. This will be a long list with a LOT of numbers. You'll also need the zip code of the place that is doing the work and the name of the lab if they don't do the test internally in the doctors office. take the big list and call the insur co. Go through each one with the cost one by one. If your insur co says that the cost is high ask them what they pay because that's all they'll reimburse for unless you want to go to the next step of fighting them about it. Find out if that provider is on their list and if not, ask them the name of one that is. ie they may say that lab A is not approved but lab B is. Then call the dr back and ask if they can work with lab b. they'll probably say something like they think that lab a is quicker and more reliable but beg if you have to.
Mind you, every time you see the dr you'll have to do this again and pray that the dr doesn't want to do something they didn't put on your list when you get there.
Have you tried an autism support group on the subject of leaky gut for provider info, insur co info and such? As you know from this waiting list nonsense, there are a lot of parents doing this who have a lot of valuable info. They may be able to tell you how to negotiate between the dr and the insur co. eg I had one specialist give me a bill for $400 listed as speech therapy. insur co paid it at $75 based on the codes on it. I went back to both and said look... we were there for 3 hours and I'm getting a 25 pg report. How can you say that's worth $75 which is one hour of reg speech therapy? We added codes for oral motor therapy for an hour, written evaluation time, etc, etc and amazingly I got to the $400 easily! So just talk to them.