Improving acceleration using 2bbl Carburetor?

These cars run and drive fine when everything's in proper repair and adjustment. Sounds like you need more repairs and adjustments before thinking of upgrades. No, slapping on a 2bbl or a 4bbl doesn't just automatically give you better or much-better acceleration, and putting on a different kind of carburetor like this is non-trivial on a '64 Dart.

Your mechanic doesn't sound quite capable of doing what needs doing, if this is how you got the car back after he "rebuilt and tuned" the carburetor. Carburetor operation and repair manuals and links to training movies and carb repair/modification threads are posted here for free download. Follow Tune-up parts and technique suggestions in this post. And don't forget the valve adjustment.