You let them go free. "It is better that ten guilty persons escape than that one innocent suffer."
If you actually have so many people committing crimes that there are actually too many guilty people for the courts to properly try, you have a societal engineering problem, not a courtroom efficiency problem - you need to get people to stop committing those crimes in the first place, since clearly the justice system isn't working as a deterrent. There are lots of options, including changing social conditions, reclassifying the behavior at issue as not a crime, etc.
This mentality is hard to get to for a lot of folks. It doesn't just hit this issue.
Let's talk about race. When a white supremacist wants to kills some folks, sure, that's a problem and we should try to detect, prevent, mitigate, and punish (in that order) their actions.
However, the real issue to solve at a higher level is the societal engineering one where large segments of the population feel a need to turn towards white nationalism. Note: I don't mean "let's make thoughtcrime a thing". I assume the issue is that racially homogeneous rural areas end up with a combination of little welfare and little economic opportunity.
In the medium/long-run, these sorts of issues require UBI, an improved education system, public transportation, and universal healthcare of some sort. That's a tall order and hard sell, so we're left demonizing individuals (treating symptoms).
If you actually have so many people committing crimes that there are actually too many guilty people for the courts to properly try, you have a societal engineering problem, not a courtroom efficiency problem - you need to get people to stop committing those crimes in the first place, since clearly the justice system isn't working as a deterrent. There are lots of options, including changing social conditions, reclassifying the behavior at issue as not a crime, etc.