You beat me to it. Best one all round and funny too.
Sister Fidelma (author: Peter Tremayne)
A rather obscure one, and less a detective than a general problem-solver, and sometimes simply an observer who unravels a mystery but leaves things exactly as he found them: Avram Davidson’s Doctor Eszterhazy, of the Triune Monarchy of Scythia-Pannonia-Transbalkania.
To which I feel obliged to add: Decius Caecilius Metellus and Gordianus the Finder.
And did anybody mention the Hardy Boys or Nancy Drew yet? No??? Tsk, tsk. :mad:
Damn zamboniracer, you beat me to Rockford. I loved that show.
Ah, poor gumshoeing. Post 25. 
Thirded.
The two greatest TV detectives were Columbo and Rockford.
Oh, yes, the Legendary Lieutenant. Some of the best detective stories in print. I don’t know how recognizable he’d be for the purpose, though.
[aside] Have you read *Finding Moon?[/*aside]
Sure have. Got it in hardback. Very good. 
Only if he brings Hawk with him.
Morse and now Lewis
Steve Carella,but now fading fast
Frost
Sister Fidelma also starting to fade now
While technically not a detective, Johnny Smith of The Dead Zone is good at solving crimes. And Anthony Michael Hall is so cute.
What, no Elvis Cole? And the ineffable Joe Pike?
Since your goal is to present the characters as a performance, I would suggest detectives that have the greatest differences in presentation between each other. Holmes is incisive and coldly logical; Poirot is polite and diffident; Columbo appears absent-minded and has the habit of asking “oh, just one more thing.” Marlowe is the quintessential noir detective. Clouseau has the ridiculous faux-French accent going on.
But the point is, they all sound different. That’s important. So far, you have a good start on that.
If you’re feeling up to it, another detective duo you can add to your list are Shaggy and Scooby. They certainly have a distinctive sound.
And I second the nomination of Charlie Chan.
Come on, no Inspector Clouseau?
See both the OP and the post immediately before yours
I love these “List the greatest…” threads, it’s so easy to miss one item on a two page list. 
My current favorite: Aloysius Pendergast.
The crime-solving Rabbi Small.
Precious Ramotswe from the No. 1 Ladies’ Detective Agency series.
I can’t believe nobody’s mentioned ___________________!