We do have multiple such methods. Just some of the procedural protections that exist for the accused:
1) Evidence can be suppressed for numerous reasons due to police misconduct or even honest mistakes.
2) Prosecutors have an ethical obligation not to bring bad cases. They can be disbarred if they do (e.g. like the prosecutor in the Duke basketball players case).
3) Prosecutors must get a grand jury indictment to bring a case.
4) The defense can motion to the judge to exclude evidence that would unfairly prejudice the defendant.
5) The jury must convict.
6) The defendant can appeal to the Court of Appeals (in the federal system) or the equivalent.
7) The defendant can appeal to the Supreme Court or the equivalent.
8) After losing all appeals, the defendant can file one or more habeas petitions to collaterally attack the judgment.
9) The defendant can petition to set aside the judgment based on new evidence that would have changed the jury's verdict.
I'm not well-versed in criminal law--there are a raft of other ways to attack convictions. And the convicted do use these avenues. A substantial fraction of the federal dockets are habeas petitions that have no merit but must be heard as part of the process of ensuring justice.
Before you add yet another "protection" by allowing the convicted to sue prosecutors, you have to think about what it would do to the system when all the actually guilty people started filing those suits. Does it really add to "justice" more than it burdens an already strained system?
Remember: prosecutorial immunity does not keep people in prison wrongly--it keeps those people from subsequently suing prosecutors for damages. Moreover, where do you set the bar for liability? If you set the bar too low, e.g. allowing suit when you simply think the prosecutor was too harsh (as in Swartz's case), then you basically make prosecution impossible. If you set the bar very high, you end up actually punishing a very small number of people (e.g. prosecutors who manufacture evidence to get a conviction), but you still create a huge number of lawsuits from those that are justly convicted.
I don't necessarily disagree with you, but imagine we gave (2) more teeth and a greater frequency of enforcement. You don't have to put the ability to initiate such proceedings in the hands of defendants so long as the people who can do it are fully independent and properly funded. Which is not a solved problem, granted, but it could conceivably be worth investigating solutions to it.
And am I the only one who found it alarming the extent to which the plea bargaining system eviscerates almost the entirety of your list? If someone innocent pleads guilty against the expense of a trial or the risk of an order of magnitude or more higher penalties, how many of those safeguards disappear? Suppressing evidence becomes irrelevant, no jury, no appeals, what does that leave? The Grand Jury that would indict a ham sandwich?
I guess my impression was that you can not go to far down that road starting with only $60,000 in the bank unless you have a good lawyer take you on for free which is uncommon.
Meaning these options are not realistically open to large percentage of the population.
That much money would hire a competent criminal defense solo-practitioner for enough hours to work through many or most of those options. And for those who can't afford it, at the federal level public defenders are similarly credentialed as prosecutors and are by law paid the same (for obvious reasons). And there is always pro se representation with the help of legal aid clinics and prison law libraries. Prisoners with no money file huge numbers of appeals and petitions every year using these resources.
Now, Aaron Swartz did blow through a ton of money defending himself. But he also hired an entire team from one of the top white collar firms in the country. Moreover, his case was complex. He couldn't very well argue "the DNA says someone else did it!" He was a political activist engaging in civil disobedience. He was stuck arguing that while he did what the prosecution claims he did, what he did shouldn't be a crime. You can't really extrapolate from his case to argue that it's impossible to take advantage of the various procedural protections because of the expense of doing so.
And as such, should have multiple methods of finding and remedying instances where this is the case...
If a system of justice is systematically unjust; it can hardly be called a justice system.