How do I get rid of smells and tastes leaching into other cookies when stored together for gifts?

The only way you're going to accomplish that is to (shrink)-wrap them individually or to put small hermetically sealed tin or plastic boxes inside a larger box...

Mint is just too powerful not to leach into everything and that's why the professionals:

• shrink-wrap them individually or per type
• sell a box per type ("Chocolate cookies", "fruit cookies" , ...)

_{Sorry: probably not what you wanted to hear...}