I read your posting with interest, As I have been fighting Amalgam illness, a bad root canal, and other issues for several years now.
I would say address the gut issues at the same time as doing chelation. If you just chelate without addressing your gut issues, you will be very weak and it will be extremely hard on you.
first off, you should wait a bit before starting chelation. I think Andy's book says 3 months.
Second, You should try different things like enzymes for mal-absorbtion, pro-biotics to correct bowel flora, and coconut oil ( organic, virgin is best ) to kill yeast, parasites, and infection. Kefir and Yougart in small amounts may also help.
In my experience, you can chelate over and over, but until you address parasites, yeast, and gut flora problems, your heavy metal problems will keep returning.
I've also found that taking dozens of supplements doesn't help either, if your gut is all messed up.
If your Naturopath doesn't believe in these problems, get another. Gut problems go hand in hand with Amalgam illness. My gut was like a cesspool after I got my fillings out. I can't believe some of the parasites I've seen come out over the last 3 years. Tapeworms, flukes, roundworms, "blobs" of yeast, etc.
Your naturopath doesn't know squat about Amalgam illness if he doesn't believe in malabsorbtion and gut problems. You want someone who knows everything about heavy metals. Or you can try to chelate on your own, carefully and slowly.
But a counter point, regardless of which Naturopath you use, be wary of naturopaths charging tons of money and putting you on tons of supplements. Too many supplements can throw your body so out of wack, it does more harm then good.
Note, I also found infrared spa's and NAET someone helpful. A good sauna a couple times a week to start will help sweat out heavy metals and toxins.
Also, I found that excluding meat/animal protein from the diet while detoxing heavy metals was extremely hard and difficult on my system.
One more word of caution. Don't focus too much on pulling the heavy metals out. Look at the big picture. Look at other ways to improve you life like, better diet, stress reduction, excercise, using more natural products for bathing, washing, cleaning, praying to God, giving to charity, helping others.
Amalgam illness is a warning. Its your body telling you to change your life.
A slow, easy detox is much better than a fast, reckless one.
Also, I would be very careful using DMPS or DMSA. I refuse to use them. I also tried and didn't have great luck with ALA and don't use it either.
Its made my detox take a while ( 3 years ), but my kidneys and liver are in good shape and working now and I don't have to worry about man-made crap getting stuck in my system. Note that ALA is man made, and only R Lipoic Acid actually matches the Lipoic Acid in the body, so I quit using ALA.
Hope this helps. Its only the sum of my experience. Your experience may be different, but hopefully my words will help you make the right choices you need to make for your healing journey.