OK, I found at least one solution on the Font Squirrel side.
If I select Custom Adjustment and define the same Ascender and Descender properties in Glyph Min, then I get the icon to occupy a perfect box.
I’m not clear if there is something still going on with how I’m constructing the font on the Glyph mini side, but at least this is a fix. Hope this is helpful to anyone else who might encounter this problem.