The USMC Harriers were, however, built under license by a US aviation company. Ditto a bunch of other British-designed aircraft used by the USAF, such as the English Electric Canberra aka Martin B-57 Canberra:
I don't know the military purchasing requirements, but it might be that there's no way to get around it using shell companies.
The State department handles this, right? I suppose that's why defense companies like Lockheed Martin donate a lot of money to certain political campaigns.