How do I duplicate multiple layers but keep them from switching groups?

If you always have exactly the same structure in the Layers panel then you may be able to automate that task. All groups must be one above another and expanded plus all layers and groups must be visible in order to automate task using actions.

When recrding action it is recommended to use keyboard shortcuts to select layers and to move through layers because hard coded layer names which are recorded when you click on layer/group will require layers and groups with the exactly same names to be present in the layers panel.

I see the problem that you describe, but there doesn't seem to be a way to get around duplicating them one at a time. The Command-J or Control-J shortcut could speed up the process.