Allow me to humbly step into this long standing debate with my personal opinions.
I hardly can take the point that Augustus was not a monarch.
I do agree that we cannot discuss about the Roman Republic in terms of the modern definition of a Republic, but saying that the Republic hadn't gone anywhere... well, I find that quite hard to agree with, unless, and I know that's a provocation, you take the point of view of Caesar, "nihil esse rem publicam, appellationem modo sine corpore ac specie" (Suet., Life of Caesar, 77) that the Republic is nothing but a mere name, without body or form. And yes, I know that dear old Suetonius is not a very reliable source...
Now, in this sense, I could agree that the Republic was still in place under Augustus, otherwise it seems quite hard to get along with your statement.
August had, effectively, taken upon himself so many power and rights, that he was running the State on his own, leaving the Senate without much to do or say, other than agreeing with him.
As to why he never admitted that the Republic was gone, I stand with Indianasmith... he saw what happened to his "dear old great-uncle Julius".
But I do agree with Caldrail about the fact that the nasty side of Augustus is rarely focused on, which something that really makes me angry when I read about him! Everybody horiifies at Sulla's proscriptions, but when it come to Augustus' proscriptions many authors tend to underplay them. Why? He even put some of his own relatives on them (true, most of them got away with their life, if not with their money), but still we are talking about a boy in his twenties... I find it quite indicative of what kind of person he was.
About Augustus duality, it comes to mind a book I read some years ago, by an Italian journalist and writer - not a historian - who had a big passion for Ancient Rome and studied and wrote on it, Antonio Spinosa. The book was "Augusto, il grande baro", which can be translated in Augusts, the great cheater (or mystifier, if you prefer)...