your symptoms are exactly what I've experienced, all fine until accelerating uphill, which is when the carb is flowing the most fuel, much more than sitting still reving or cruising on the flats, because the engine is loaded more, using all it's power .... it starts right back up because it only takes a minute to get the carb gas level back up again, it's pumping, just not pumping max volume .... it may be that the cam lobe is worn, in which case you might need to build up the pump lever slightly [spot of weld], which is what I did with a used pump after experiencing the same symptoms with a 2nd original pump - and keep in mind that those "new" pumps are more likely "re-manufactured" so the arm ends may be just that silly millimeter shorter and your cam is likely 50 years worn
Bill