Cheers for thoughtful dialogue on the Internet!
I should be clear: I don't personally support what the DOJ is doing to Assange. I even think the Espionage Act likely has Constitutional defects as applied to his case; it's just never been tested. And I think the Espionage Act should be repealed at the earliest possible moment. That being said, I think we're stuck with it, and our Constitution likely doesn't prevent it from being a law, albeit a bad one.
On the other hand, I have serious misgivings about the false statement laws, at least as they cover unintentional false statements (i.e. those without _mens rea_). I don't think our Constitution was meant to punish people criminal for actions that they aren't even aware of. Unfortunately, there is long precedent establishing that "strict liability" is permissible even in criminal law. It seems like a gross violation of due process to me, but unless and until something changes, we're stuck with it.
I think you've also hit on a much bigger problem I have with the justice system: this fairly absurd idea that law enforcement can do nearly whatever it wants, whenever it wants in order to seek its own ends. If I were to propose criminal justice reforms, I would focus first almost exclusively on police procedure. Forget about bail reform or sentencing guidelines: don't allow cops to lie to people while performing an investigation; strictly prohibit cops from making any innuendo that someone waiving his or her rights is somehow "looking guilty" or some such nonsense; and get rid of the plea bargaining system.
Essentially the only thing anyone should ever say to law enforcement in the US is, "I refuse to any questioning without my attorney present." Anything else you say to them can and will be used against you, and cannot be used for your defense, since it is hearsay. It's not too hard to see that the distribution of people who know how to respond to pressure from the cops to talk is heavily skewed toward the less privileged segment of the population. When you add in things like plea bargaining, which has resulted in even many innocent people pleading guilty to crimes they didn't commit, I don't think anyone can call it justice.
It's late so I'm rambling, but I think there are serious problems with the justice system. I just don't think Chelsea Manning is a particularly great poster child for them.