I love your stories, Sharon. Great article.
I have had quite a few different mints in my garden over the years. Most aren't too invasive here, but I guess they could take over if left unchecked. My catmint and bee balm do spread a lot and each spring I rip out a lot of the root mass to keep the plant clumps at a reasonable size. I have had spearmint over winter in a window box. The peppermint did not.
I have grown Korean Mint a few years. The leaves are quite small and bluish. Tastes like licorice
I haven't tried it, but my neighbor says that chocolate mint on vanilla ice cream is quite yummy. The chocolate mint seems quite hardy here, but I don't consider it invasive. I usually have to search for it in the flower beds when my neighbor want some for ice cream. I have also grown Majito mint, for making a Majito rum cocktail. I guess it would be similar to your whiskey julep cocktail.