The solution lays not with the accused, but their lawyers. The lawyers can simply refuse to defend cases and the system will crash. And no one, no poor defendant, will risk jail. In the 1960's there were "committed" lawyers who took a stand against the Draft, as well as legal organizations that took a stand--the National Lawyers Guild comes to mind. Unfortunately, the idealism of the 1960's turned to drug defense work in the 1970's and by the 1980's the pendulum had swung back and hard.
Even if only a small group of lawyers refused to handle cases, such as federal Criminal Justice Act attorneys (18 USC 3006A) the system would not be able to cope.
Unfortunately, it's easier to herd cats than to get lawyers to act in unison. But this is a better solution than asking the first few defendants to risk life sentences: no one wants to be the Wildebeest that enters the crocodile-infested river first. But a work stoppage by these lawyers would carry little risk of consequences other than a serious reassessment of the broken US criminal justice system.