Nitpick…jeopardy attaches at a bench trial when the first witness is sworn in. If you had a document that didn’t need authentication by a witness, as far as I know introducing it wouldn’t attach jeopardy.
Well, since Blockburger is no longer the law of the land, it doesn’t really matter. It was replaced with Grady v. Corbin, 495 US 508 (1990). Then it was replaced with US v. Dixon, 509 US 688 (1993). Dixon reinstated the “same elements” test that had prevailed since Blockburger, but strictly speaking Blockburger is no longer the controlling case.
Different sovereigns can of course both prosecute, unless the second sovereign to prosecute is the federal government (the Petite policy.) That policy must have failed in the case of the LAPD officers of the King incident. As for multiple offenses, the three tests used in varying courts for double jeopardy:
1.) “Same elements”: it is not a double jeopardy infringement if each offense charged requires proof of a fact which the other does not. Example: Not allowed under this test is to convict for assault&battery and murder. All the elements of assault and battery are in murder, murder just has an extra (the death of the victim.) Thus there are no elements of a&b that aren’t in murder, so no-go. This is the Blockburger and Dixon rule, the SCOTUS holding, so the law of the land in FEDERAL courts.
2.) “Same conduct”: the same conduct cannot be used twice as an essential element of the crime yielding conviction. This was the Grady rule, in effect in federal courts from 1990-1993. Since it is more protective of criminals’ rights, the states may interpret their own versions of the 5th Amendment to use this test rather than the “same elements” to extend further protection to the accused. About a dozen states use this test.
3.) “Same transaction”: rooted ideologically in Brennan’s dissent in Ashe v. Swenson, 397 US 436 (1970). All offenses that “grow out of a single criminal act, occurance, episode, or transaction” are considered the same offense. Common example is that if B kidnaps, rapes, then murders C, and B is prosecuted and convicted only on the kidnapping charge, B cannot later be prosecuted for the rape or murder of C. Only half a dozen states use this test.
So there’s what you’re up against. I think that, rather than amend the double jeopardy clause, it would be wiser to simply legislate one of those options that you find most pleasing. That would make it the law of the land in federal court. You can then work in your state legislature to alter which test is utilized by your state courts.