Grounding is not needed for any box that has no working electronics inside with electric connections to the outside. It only causes trouble.

This wire will not change much as there is no effective way to prevent long conductor with such energies acting as an antenna. Big ferrite coil prevents high frequency currents from flowing, but with such energies, sparks would pass through air dramatic distances and only ceramic insulators, no worse than the ones on high voltage lines would make a difference which makes it not the way to do it unless it's installation with antennas requiring grounding and worth investment for numerous workarounds.
Usual solutions are to make extremely thick wires to the ground so that worst possible EMP would not melt and harden EMP protection a lot. Every external component is then interconnected with a much thicker wire so that currents from different grounds would not make sparks traveling from every grounded device. It makes lots of ground loops, uses up lots of metal for wiring and there is no guarantee that everything will not melt with higher power EMP than expected.

Protection principles are completely different from simple Faraday cage, where you can have DC current flowing inside and extremely low voltage as metal resistance is small. With AC current is changing with time. As current flows with the speed of light, by the time current flows from one end of the box to the other, current changes. Once current changes, there is voltage change too. The higher frequency, the more voltage and current changes by the time it travels from one end to the other. It means that with certain frequency you can have huge voltage differences inside the cage if AC current flows which is not happening with DC in Faraday cage. With DC you can have high voltage charges that can spark from one point to the other, if they are not connected by wire. Grounding is important. With AC you are making voltage differences by connecting any wire or conductive extension through which current can flow or you are making an antenna.

Skin effect is the only thing protecting from EMP in metal casing as it makes high frequency currents travel only through thin surface layer of metal. If you have solid metal box, currents appear only on the outside surface of metal case and cannot pass to the inside part. Part leaking inside is extremely small. Current fades exponentially with depth. The higher frequency, the thinner is surface layer. By increasing metal thickness EMP protection becomes better against lower frequencies that have thicker current layer on the surface which leaks then less inside.

There is no strict requirement to use insulator inside the box. Inside surface can be understood as a current loop. Problems rise when there are leaking significant currents inside the container. Once you have a device touching this loop, it becomes part of it and currents start flowing through the surface of device and in worst case scenario, they get inside and do something bad. Usually device is much smaller than inner perimeter making it extremely bad situation, currents of a big loop passing through a small protected device. Even if there is no contact and device is close to the flowing current, currents are induced inside the device too. It is a better situation, but non the less not desirable. The best way is to put any insulator that would keep device not only insulated, but also at some distance from walls.