I have found the solution to keeping berries last, and for those of us who are spending our children's inheritance on blackberries and raspberries, this is magic. I knew I had to tell the people!
Step one: Soak in baking soda and water for 15 or so min
Step two: drain, then let them sit on these towels, and gently pat them
https://www.onceagainhome.com/
Step three: store them in these containers when they are super dry
https://www.amazon.com/stores/Snapware/Homepage/page/F5616D0D-8355-49C3-8072-765478692831
It's a berry miracle. Raspberries last two weeks, useful when "we hate those!" this week, and blackberries are the preference.