My 72 Duster acted just this way years ago when I rebuilt the carb. It turns out the base gasket supplied with the kit had sucked up into the carb base, and was blocking off the vacuum passages under the carb. I put the old gasket on, and fixed it. Turns out the underside of that carb is really important. At the time, my wife was driving that car to work. Boy did I get a boat load of crap for that one.
Wish I still had that car! For what it's worth, the car pictured in this signature, for five years had the set up on it that you are trying to get to work now. It worked beautifully. It idled nicely, and got great gas mileage. I especially liked the adjustable metering rods. I tried many other two barrels on it, but always came back to the BBD as the most flexible, and easiest to tune. If that carb does not work for you, try another one, or try rebuilding tht one yourself. My carb was just the two barrel that came off the junk car I got the manifold off of, which I then rebuilt.
Sandy's comment about the play around the throttle blade shaft is important. They are prone to wear, and will leak when they are worn.It kind of sounds like maybe your float is too high. If you did rebuild it yourself, you would get an instruction sheet with the rebuild kit which would tell you how to set up the metering rods, float levels, etc, etc.
Sam