I am not a lawyer. That said, here are a few comments on how I understand things and where I think they'd go. Your mileage may vary.
I always chuckle at this sort of thing. I like to call this "The Reiser Defense". If you ever followed the Hans Reiser trial, you'll note that he had a fundamental misunderstanding of how law works (or even is supposed to work). As a developer, he saw laws as a program. He thought that he had the program set up so as not to be able to convict him.
As it happens, the Law is not a program or set of mechanical rules. The Law may *appear* to be that way, but that's mostly a side effect of one of its goals. The Law is intended to be predictable so as not to be perverse when applied to people. The theory goes that people can only be held accountable for breaking laws if they can reasonably have been expected to know that they would fall afoul of it.
As it happens, this is not a blank check. You have responsibilities not to be entirely ignorant of the law. You have responsibilities to cooperate with law enforcement and the Court. You do not get to interpret the law any more than is necessary to mount your defense. All of your interpretations are subject to validation and endorsement by the Court. So the process surrounding justice use the trappings of a program or set of mechanical rules, but that is largely a construct to allow you to cooperate with the Court in executing the upholding the intent of the Law.
In fact, it's why it's called Contempt of Court. You have rights under the Law. It's the Court's responsibility to uphold those rights for you. Criminals do not respect the Law. If you behave in such a way as to prevent the Law from being applied by the Court, you show contempt for the rule of law and you hurt your chances in being able to exercise your rights under it. This is a fairly obvious social contract, and that contract--not some expectation that the law function as some sort of autistic machine--is what fundamentally underlies Due Process.
The Fifth Amendment is a law like any other. It's intention is to ensure that the parties involved in justice maintain separated duties. The theory is that you and the prosecution make claims and the court evaluates those claims. If the Court were permitted to compel you to make certain claims, then it's no longer really evaluating them and the integrity of the system breaks down. That's the context that Fifth Amendment lives in and that's the context within which Courts will evaluate it. It is not a "technicality" that gets you out of cooperating with warrants. So, while the law cannot force you to say something is true or false against your will, it *can* compel your cooperation in unlocking the filing cabinet containing the evidence that implies the same thing. That's the difference, evidence is different from testimony.
There is a bit of a grey area around combinations / passwords. This is largely due to prosecutors abusing your unwillingness to give them unfettered access to something as being parleyed into some kind of claim of guilt. That's what the Fifth Amendment addresses--your lack of a statement cannot be construed as a claim of guilt. This started with a dissent from the Supreme Court that mentioned that giving up the combination to a lock amounted to testimony that you had access to what it protects. It's similar to a different case where the prosecution subpoenaed "all of the papers that apply to " and the 5th was upheld as saying evaluating which papers were submitted papers would be tantamount to asking for testimony that some of the stuff was illegal. That fine line between testimony and your duty to comply with the collection of evidence by authorities is something best discussed with a lawyer, because it is not a silver bullet.
I believe that your unconventional take on copyright law isn't likely to get you anywhere. You're effectively claiming that Copyright Law puts you in a 'guilty until proven innocent' which is, more precisely, claiming a violation of due process. This blanket claim has never been supported by a court, mostly because Courts don't share your interpretation of Due Process or Property Law in general.
Consider by analogy that you're found in possession of someone else's car. It's legally registered to them. You're found in possession of it. You're allowed a defense. If you don't make the case, you're guilty. How is the copyright case any different? While I'm quite sympathetic that possession of a car is different because you can't flawlessly duplicate a car, I don't know that it addresses the fundamental fact that you possess it and you can't substantiate permission to have it. That's not so much a claim that the possession didn't happen but rather that it's so easy to do that the concept of possession is meaningless.
Less abstractly, a real case comes with real context that often prevents it from hinging on anything even half that abstract. Your claim that you can't prove purchase exists among a sea of verifiable facts. How much other possibly pirated software lives along with it? How is it packaged? Is there any evidence that you downloaded it from a site that pirates software? Can you show bank records of a purchase that's roughly the right amount? None of this stuff lives in a vacuum. There comes a point where there's enough context to convict you.
Circumstantial evidence isn't, by itself, prohibited. Judges largely exist to navigate this sort of thing. Outright defying otherwise legal warrants to gather the evidence to convict or exonerate you harms your case. Compelling you to say "I stole software" is illegal. Compelling you to allow search of your garage containing a half-a-dozen cars that aren't registered to you is not.
The simplest legal defenses are often the best. I think you'd get more traction out of the Fifth Amendment defense by itself than trolling Copyright Law. As a matter of law, I'd expect a judge to just blink a few times and call that defense irrelevant. More precisely, your opinions about Copyright Law aside, trolling the judge is always a bad idea, because (other than your lawyer) the judge is the only other person in the Court room who has a duty to protect you--and they're the last line of defense at that.