Yeah well they think NERV is trying to start 3I and they only have so many N^2 mines. Take a guess what they'd pull out next and keep using in an attempt to stop NERV and hope all the while they don't cross a bad threashold.
If their as trigger happy with the nukes as you think they would be, there may be a way to use that against them. Since EOE unit 01 has flight capability, I would have the option of taking it into the upper atmosphere. If a nuclear device goes off at a high enough altitude, it'll send out an electromagnetic pulse powerful enough to disable electronic devices and take out all power below. If a single large nuclear device were detonated over north America for example it could take out all the power and electronic devices in the whole country.
What I would do is fly over each country and begin attacking the military using the lance, then once they fired off the first few nukes at me I would leave and fly higher outside the earths atmosphere where it would no longer be practicle to attack me and then move onto the next country since the one I was just at would be incapable of fighting since all their technology would be disabled from the EMP pulse given off by the bombs.
Of course once this is over with there's still the possibility that there may be some nuclear capable subs and bombers leftover, but they wouldn't know what exactly is going on since they couldn't communicate with their countries military.