[thaumasiotes]

> In my subjective experience, French and Spanish are by far the closest of any two of those languages.

This is precisely what you would expect from the divergence times.

> Cantonese and Taiwanese would be the next closest and Mandarin is considerably further from either than they are from each other.

This isn't; Taiwanese is the outgroup to the more closely related pair of Mandarin/Cantonese.

It's always possible that learning "a bit of Cantonese and a bit of Taiwanese" doesn't give you a good grasp of what's going on in Cantonese and Taiwanese.