Trouble Starting after sitting

I've been having a reoccurring issue since May with my car refusing to start after sitting more than 5 days. I used to be able to let this car sit for months at a time and start it up with only one pump of the gas pedal. Now, I can't let the car sit more than 3-4 days, or it won't start without pouring gas into the carburetor.

The fuel pump was replaced in May, but the starting problem was happening before that. I replaced the pump and filter shortly after the problem started thinking this was the cause, which it may not have been. I'm thinking about purchasing a rebuild kit for the carb, but I'm not sure if this will fix the problem or not. I think it's an issue with fuel not getting to the accelerator pump, or not enough is in there to begin with. Once the car is started, after pouring gas in the barrels, car runs fine and will start with no issues for the next 3-4 days. No issues with the carb while driving the car, no stalls, hesitation, etc. I've checked and adjusted the float level, but this hasn't made a difference. Could a bad accelerator pump cause excessive fuel evaporation? Thanks

1968 Dodge Dart 270
273, 2 bbl Carter (stock carb)