Docs are going to be CW, and you're not going to sway them. You may impress them with improving measurables, but I'd keep your description of diet pretty simple, just say you've cut out processed foods, sugar, and refined carbs (we know that means grains), and keep it at that.
I've pretty much taken that approach, and my doc keeps telling me to keep on doing whatever I'm doing. She's said she's noticed a marked improvement, so I just kind of let her keep thinking I'm eating low-fat.
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