Comment by thaumasiotes

That would be the opposite of consistency; i is the front vowel and ı is the back one.

Note that the vowel /i/ cannot umlaut, because it's already a front vowel. The ï you cite comes from French, where the two dots represent diaeresis rather than umlaut. When umlaut is a feature of your language, combining the notation like that isn't likely to be a good idea.