69 340 problems

Could be bad gas or water in the gas (among all the other things it could be).
Try running it with a gas can with clean fresh fuel.
Everything you've described about the carb floats etc.. seem perfect except for delayed acc. pump squirt which can cause hesitation. Thats adjustable.
Only similar problem I recall was venturi bleed tube had fell out of where it is staked in the casting. Was a 2 barrel on a 318 but same condition. Engine would only try to run , poorly and briefly.