The Fifth Amendment to the U.S. Constitution
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
(highlighted by me)
IMO, the Constitution trumps some procedural detail. The double jeopardy clause was written because the founding fathers were concerned about just this issue: a zealous prosecutor retrying someone after they were found not guilty by a jury. It shouldn't matter that the jury misunderstood how they were supposed to communicate their findings, as long as they were unanimous that KR was not guilty on some of the charges.
Using technicalities to deny someone their constitutional rights is an enormous miscarriage of justice, and I would say this no matter who was on trial and how I personally felt about their guilt.