"It kind of makes sense, since the fluoride in our toothpastes disturbs the normal oral bacterial and fungal fauna, which is allowed to restore when you go off fluoride."
I haven't heard this before. What is your source?
Fluoride is used in toothpaste because it mainly helps prevent cavities. It's relationship with bacteria is more complex, and I've seen only weak evidence that it affects any balance.
If anyone is concerned about toothpaste or shampoo, a better experiment is to not use them for a period of time rather than trying different brands. Else, use a very basic substitute (e.g. baking soda for toothpaste).