My first guess would be valve seals. Once the motor is shut down, if there are bad/damaged, they would leak a little
oil down the valves and upon start-up later you would see the smoke your talking about, but 3+ minutes seems a long time to me......
Were the Edlebrock heads used on the motor new or used????
Another thing might be a leaky intake gasket. A cold engine would suck a little
oil till the engine warms up and things swell up, the leak could "seal itself".....
I'd start it up and let it run till the smoke stops then pull all the plugs and have a look see, this could tell you more about the
oil burning.....
A quart evry 1000 miles after 3900 miles is too much IMHO........
David