My theory on how to fix this is to maintain the adversarial nature of the courts. Don't force the DA to prosecute cops. Have them maintain the relationship as it currently works and let the DA become the the cops' lawyer by default while the Public Defenders' office take over the role of prosecuting police.

Since the PD and DA are already set-up this way in relationship to policing, this makes more sense than trying to wring impartiality out of the DA; they have to work hand in hand with police to convict criminals and need to maintain a cozy relationship. The simplest solution would be to keep the dividing lines the way they are.