Great that you bought a new toaster. Impossible to get those things free of gluten after years of use, I think. My personal opinion is that you should also buy a new bread machine. Even though I wash everything carefully by hand, I still notice that I sometimes miss a speck here and there. I never really scratched mine or anything, so I don't think gluten could get stuck that way, but I don't know what you do with your bread machine.
I don't think there is a gluten free setting on bread machines and if there is, I've yet to see one. That said, there are bread machine mixes you can buy, and there are gluten-free bread machine bread recipes online that can guide you in the beginning.
Personally, I hate gums (no glue in my food, please. lol). I suggest experimenting with ground chia seeds soaked in boiling water (equal to measurement of gum). It gives you a gooey, almost egg-like consistency.
Hope that helps!