So I looked up the 2B and I think that is probably your problem. Looks like it is a two barrel 500 CFM carb. The 390 can accommodate a 670 CFM four barrel carb which is what I'm running on my '64. Your car could be starving for gas because of an undersized carb.
Another thing to check is the air cleaner assembly. The stock air cleaner assemblies on these cars are cleverly designed to deprive the engines of enough air to run well. You can tell if this is the issue by running the car down the road without the air cleaner assembly, so there is no restriction on air getting into the carb.