Hello C6H8O7,
You have provided a valiant effort to fix this persons problem. Unfortunately, it doesn't look like its going to work. When you mix methanol and water, they act like one chemical.
I liked your reference. Here is the portion from your reference that provides an answer
Such enrichment by freezing of a solution in water is sometimes oversimplified by saying that, for instance, because of the difference in freezing points of water (0 °C/32 °F), and ethyl alcohol (-114 °C/-173 °F), “the water freezes into ice...while the ethyl alcohol remains liquid.” This is false, and although some of the implications of that description are true and useful, other conclusions drawn from it would be false.
Unfortunately, the ice will not freeze before the methanol does.
I like your logic and the ability to think 'outside of the box'.
Please keep up with the great ideas!
Eugene