I feel like I’m getting whooshed here, but (a) Columbo, not being in the audience, didn’t get to watch the murderer strike; most of his track record involved reconstructing events the rest of us had already seen play out. And despite that, (b) there were a number of episodes where the audience didn’t get to see whodunit, at which point Columbo showed up to ferret out the killer’s identity as usual.
Sam Vimes. Yes, even in the modern world.
monk or Vimes - either would do it…
Charles Bronson. The mystery might not get solved, but goddammit, shit would get done.
And besides, Lance White already brought the crook to justice.
Poirot without Cap’t Hastings would probably do a lot better than Holmes without Dr. Watson. There’s plenty of Poirot mysteries without Hastings – he didn’t have Hastings with him on the Orient Express.
As to Miss Marple, I think she’d do just fine figuring out who committed the crime but would have a hard time getting the police to believe her and not dismiss her as a nosy old biddy. In the stories, the local police would listen to her because they received a telephone call from Sir Somebody-or-Other, her dear old friend at Scotland Yard. 
Which leads to a question about our scenario: do the police know – and believe --that you’ve brought a fictional detective to life? In other words, do they know this really IS Miss Marple, or do they have to be convinced she isn’t a crazy old lady who’s read too much Christie? 
Luther.
Rebus
Lord Peter Wimsey. Even without Bunter to lay out his trousers and take crime scene photos, Lord Peter will get it done. Without using a mass spectrometer, just a monocle.
StG
The rozzers will accept any competent help, having no other means of catching the killer.
Sipowicz. If you let him use the phonebook.
Kay Scarpetta.
She’s the only one who can deal directly with the DB.
~VOW
Absolutely.
Brother Cadfael
Si