Improving acceleration using 2bbl Carburetor?

When I first got my ‘64 Dart, I had my mechanic rebuild and tune my carburetor as initially it required constant throttle so as not to stall.

That issue is slightly better now. When cold, it requires light throttle not to stall, when warm is 60/40 whether or not it’s needed. However, hot or cold, sometimes when going from a stop to partial or full throttle, it misses and sometimes stalls out.

Then there’s the issue that there’s slow acceleration. Any decent acceleration requires full throttle.

I’m curious if the issue of acceleration can be fixed with a 2bbl carburetor, as I’m not looking to do a full 4bbl conversion. I believe it should give me a bit more power which should help with acceleration. I also thinking that starting with a new (or newer) carb will also help me when getting it tuned, as it would be less likely there would be other issues with the carb.

What causes the missing when I accelerate? Is it a fuel pressure issue, and if so, what’s a solution to that?