Interesting. I've never done defense. What was it like?
In the real world (non-defense), I did this once in my life. We went to and independent testing laboratory (actually the premier / highest-regarded one) with our device. They put it outside, pointed a big antenna at it, and it didn't pass. We made some random changes (adding shielding of some kind somewhere; the lab had it on-hand). Things ... changed. Sometimes they got better. Sometimes they got worse. We didn't know whether we were changing, or simply the radiation patterns to better match the test setup.
We kept making tweaks like that until it passed, and that was our final, independently lab-certified product design.
If we had tested at a slightly different angle, I'm pretty sure we would not have passed. Or in a different lab. It was deep voodoo. From what the lab guys said, EMC testing almost always looks like that.
I believed them. We can't really solve Maxwell's Equations in our head, and we know so little about antenna design that predicting the radiation from a complex device is not really possible. You just tweak, adding a gasket here or ferrite bead or whatever, and pray it works. Most of the small tweaks we did at the lab, but I do recall we did some larger design change (making a signal differential or something) which necessitated going to the lab a second time with a device with a new PCB.