The battle to appeal Judge Shira Scheindlin’s ruling against stop-and-frisk is not doomed by the vow of most Democratic mayoral contenders to drop the appeal — because Mayor Bloomberg has an excellent basis to ask for “expedited review” so that the appeal can be heard in a matter of months.

Simply put, the lack of precedent for Scheindlin’s “remedy order” is so shocking, and her record of being overruled on similar civil-rights cases is so striking, that the city’s appeal is strong. And, given the undeniable urgency — so many innocent lives are at stake — there is a compelling reason for the Second Circuit Court of Appeals to grant expedited review.

Our Constitution’s bedrock separation-of-powers principle means that it’s the judiciary’s job to declare whether a police action violates constitutional rights — but even then, it remains the core responsibility of the executive branch to run government.

Thus, when a judge rules that evidence was seized in violation of the accused’s Fourth Amendment rights against unreasonable searches and seizures, the court suppresses that evidence — but it doesn’t order the police to change their procedures.

Of course, sensible police commissioners, on their own, modify procedures to conform to such rulings, since if they don’t, the guilty go free.

Here, Scheindlin went far beyond merely declaring that the stops violated constitutional rights. She appointed a “monitor” — lawyer Peter Zimroth — to:

* Draw up “reforms of the NYPD’s policies, training, supervision, monitoring and discipline regarding stop and frisk.”

* Set “milestones” the city must achieve — presumably, acceptable ratios of white and minority stops.

* Do regular “compliance” reviews and issue formal public reports every six months detailing the NYPD’s compliance with his mandates.

* Hire experts and other staff.

She also ordered the NYPD to run “pilot” body-camera programs and hold “town hall” meetings in each borough under Zimroth’s supervision.

And the city must pay for all of it until the judge rules — whenever that may be — that the “city has achieved compliance.”

In effect, Scheindlin created a whole new agency — funded by city taxpayers but overseen by her, a member of the federal judiciary — to supervise the NYPD for years to come.

To put it mildly, she has grossly overstepped the proper bounds of the judiciary.

Yes, precedent exists for using a court-appointed monitor to intrude into the administration of state and city agencies — but only in cases where suppression of evidence is not an available deterrent against violations of rights, and where delays and missteps don’t cost lives, such as in cases involving school desegregation and discriminatory hiring practices.

Courts have never before tried to seize control of a police department’s efforts to fight violent crime. (Shamefully, the federal Justice Department filed a brief saying otherwise. But all the cases cited there involved consent decrees, wherein a city agrees to a monitor — not a court ordering one over the city’s vehement objections.

Scheindlin seemed to recognize this vulnerability. She wrote two separate opinions. The main one, 192 pages, ruled that the NYPD’s stop-and-frisk procedures violated constitutional rights; the second, 36 pages, appointed Zimroth and set up her own ongoing supervisory role. Did she want to give the appeals court the option to uphold her main ruling even if it reverses her “remedy” order?

The normal appellate process could take a year or more; the city needs to ask the Second Circuit to expedite the appeal and issue an interim stay of Scheindlin’s order.

Stop-and-frisk is a vital component of the NYPD’s proactive policing, which saved more than 12 lives a week for over a decade.Hundreds of innocent lives — mostly minority — could be at stake.

And the appeals courts have had to slap down Scheindlin before for her far-fetched expansions of the Bill of Rights:

* Osama Awadallah testified before a grand jury that though he met with the 9/11 hijackers, he couldn’t remember their names. She dismissed perjury charges against him and ruled that his detention was unlawful.

* Judith Clark, a Weather Underground radical serving 75-to-life for the murder of a Brinks guard and two cops during a robbery, wanted a new trial, arguing that her Sixth Amendment right to counsel was violated — when in fact she’d refused counsel and insisted on representing herself. Scheindlin granted the new trial.

In both cases, the Second Circuit later reversed Scheindlin.

If Bloomberg seeks an expedited appeal and stay, that request likely will be heard before he leaves office Jan. 1. Would a new mayor than dare to drop the case, and strip the higher court of its stated willingness to quickly resolve Schiendlin’s life-threatening ruling?

Stephen B. Meister is a partner at Meister, Seelig & Fein LLP. He has won one case before Judge Scheindlin and successfully defended her ruling on appeal.