I need a way to automatically make Panel layouts responsive
I think the closest you're going to get to out of the box is Panels Extra layouts, which ships with a bunch of adaptive layouts.

Other than that, your best bet is just to create a bunch of custom layouts by yourself, with their respective templates. The documentation is not bad for that; you can find it here: Panels 3: Creating a custom layout in your theme. Alternatively, just look in the Panels codebase for their implementations.