Wow, I have my collection displayed the same way.
Sorry to hear about the damage. You might be able to restore the boxes by ironing them with a sheet between the box and iron, but the laminate might peel and glue unstick. If they're MOSC then I don't think they're fixable.
Which brings us to where we are today...
Sorry to hear this Jay, luckily not your most prized figures
At least now you get to open some up !