I hope all your carb needs is a good cleaning.
However, I have the same carb on my '65 289 and have the exact same problem -- it is my LH (meaning driver's side) a/f mixture screw that it almost completely non-functional. Finally took it to a carb shop (where they cleaned it and did some other work) and they told me someone (me?) must have screwed the screw in too far at some point and reamed out the seat. According to them, there is no fix. So what I did to get it to run as well as possible:
1. with engine off, turn both screws in to a very gentle snug fit, then open both one full turn, 2. assuming engine will now start (if not, open both slightly more), begin opening the bad (d/s) screw to get the best idle possible (knowing that at this point the motor is still running rough), 3. move to the passenger side (p/s)screw and adjust that to get the best idle.
I found that once I've finished with the p/s screw, further adjustments to the d/s screw have no effect.
Per the carb "experts," this problem with the seating of the adjustment screw is not uncommon on these carbs. I'm able to get my carb to run fairly well, but I hope to eventually go back to an Autolite 4100.