> above that boiling point you distilled out all methanol (with a mix of ethanol)

That's not what studies have shown. Methanol boils off in all phases of distillation, and remains in high concentration at least halfway through.

https://pubs.acs.org/doi/10.1021/acsfoodscitech.3c00627

https://pubs.acs.org/doi/10.1021/acsfoodscitech.1c00025

Thank you for finding these! I remembered they existed but not where