I'm skeptical of this project. Existing unambiguous notations for mathematics do not start from the chaos of human conventions and then try to impose order. They start from rigorous unambiguous syntactical and semantic foundations; from programming languages basically.
For example, when writing y = |x|^2 - 1, the fact that |x| is a function application of "abs" is the least of your worries. Even given that fact, you can disambiguate into a rather large variety of mathematica expressions. Perhaps you're defining a parametric curve, perhaps you're computing a boolean value for the comparison, etc, etc, etc.
The notations of these things are essentially unambiguous in the first place, since overloaded operators rarely have compatible type signatures, and when they do, the shadowing is just shy of explicit. Human mathematical notation is definitely very bad, but not because it's wildly ambiguous, it's because it's inconsistent.
For example, when writing y = |x|^2 - 1, the fact that |x| is a function application of "abs" is the least of your worries. Even given that fact, you can disambiguate into a rather large variety of mathematica expressions. Perhaps you're defining a parametric curve, perhaps you're computing a boolean value for the comparison, etc, etc, etc.