He's not yet 2yo so it's possible his allergy tests are not yet going to be accurate because their immune systems are still cycling up and down until somewhere around 2yo as maternal antibodies are washing out and their own immune systems are maturing. It's the main reason infants get so many rounds of vaxes (because their maternal antibodies are not always fully flushed out--so those are fighting the vax instead of the child's body fighting it, which would build the immunity ). Plenty of doctors DO it, but it's kind of a lost cause because you can't rely on the results. It also depends on what kind of tests they ran (IgE, IgG, IgM?).
You're dead on: do NOT try more than one thing at a time because you won't know which thing cause the reaction (good OR bad). But I would definitely go back to journaling on him through the process. It will make your life way easier. If you want to pm me your e-mail addy, I have a spreadsheet that prints out to 1 page that you can just print off and run copies of to put in a report binder/cover.
Leaky gut is usually caused by intestinal yeast overgrowth that goes from it's normal state to a colonization that pokes holes in the intestinal walls and not only disrupts digestion, but can also "leak" undigested proteins into the body that sit on the neuroreceptors in ways that interrupt neurological connections or development and can cause behavior and development problems in children, headaches, sensory problems, etc. It's a big deal.
I would stick to whatever he can tolerate first and add a good probiotic. I would also be careful to find out what your dietitian's background is as many of them are very USDA regimented in terms of diets. I had to work long and hard to find a nutrition program that was considerate of nutrition theories that didn't agree with our government.
Once you've got him on a daily probiotic for a few weeks (maybe 3?) you could introduce dietary enzymes. They may or may not work.
If you're seeing a doctor that gave you this diagnosis, I'm kind of surprised they didn't prescribe Nystatin to you. It's not uncommon. That being said, it can also cause vomiting if the intestinal yeast is bad.
Best to you