1969 Carter AVS
George
Back in the day when my Dart was bone stock I had the same problem with my AVS. Like was mentioned before, you have a float issue. I've worked on these carbs a lot over the years and they are pretty simple to deal with. Even though you had a reputable guy go through it, check the float level and float drop. Also the tang where the pins slide through to hold the float in place need to be perfectly parallel and square to the supports. I had one float that on one side the tab was ever so slightly twisted that it would catch and stick if the stars in the sky were in perfect alignment......yeah you get my drift. Took me a while to find it because when I would have the top of the carb off and invert it, the floats seemed to move freely up and down.
What I found was that one tab had a litlle bit more side to side clearance to the side support allowing the float to move to that side and drag just enough to hang up. I'll never forget that hassle. After I made sure that both floats had jsut right amount of clearance and that the seats were good and tight, my problem went away.
Be sure to check the that the seats have gaskets on them and that the floats are good and straight to the housing.
Just a few ideas that worked for me. I'm sure there are some others here that have had some personal experience also and can offer some advice.
Good Luck!