No moonshine is mostly corn mash, if I recall. Never tried to make it. I own a still but only for distilling water and I don’t have the extra condenser part (forget the name of it) that you’d need for making alcohol.
I don’t think you need any wood product to get methanol. It would probably be present when making any ethanol. I’m sure there are some where who have expertise in this.
Mash yields a small amount of methanol which boils at 151 degrees versus ethanol at 173 degrees.
By distilling first at less than 173 you can discard the methanol.
Wood alcohol is made from wood products and produces methanol.